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8th Grade
3D Geometry
2015-11-20
www.njctl.org
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Table of Contents
· Prisms and CylindersVolume
· Pyramids, Cones & Spheres
Click on the topic to go to that section
More Practice/ Review
3-Dimensional Solids
Glossary & Standards
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Table of Contents
· Prisms and CylindersVolume
· Pyramids, Cones & Spheres
Click on the topic to go to that section
More Practice/ Review
3-Dimensional Solids
Glossary & Standards[This object is a pull tab]
Teac
her N
otes Vocabulary Words are bolded
in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.
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3-Dimensional Solids
Return toTable ofContents
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The following link will take you to a site with interactive 3-D figures and nets.
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Polyhedron A 3-D figure whose faces are all polygons.
Polyhedron Not Polyhedron
Sort the figures into the appropriate side.
Polyhedron
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3-Dimensional SolidsCategories & Characteristics of 3-D Solids:
Prisms1. Have 2 congruent, polygon bases which are parallel to one another2. Sides are rectangular (parallelograms)3. Named by the shape of their base
Pyramids1. Have 1 polygon base with a vertex opposite it2. Sides are triangular3. Named by the shape of their base
click to reveal
click to reveal
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3-Dimensional SolidsCategories & Characteristics of 3-D Solids:
Cylinders1. Have 2 congruent, circular bases which are parallel to one another2. Sides are curved
Cones1. Have 1 circular bases with a vertex opposite it2. Sides are curvedclick to reveal
click to reveal
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Edge Line segment formed where 2 faces meet
Vertex (Vertices) Point where 3 or more faces/edges meet
3-Dimensional SolidsVocabulary Words for 3-D Solids:
Polyhedron A 3-D figure whose faces are all polygons (Prisms & Pyramids)
Face Flat surface of a Polyhedron
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Sort the figures.If you are incorrect, the figure will be sent back.
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1 Name the figure.
A Rectangular Prism B Triangular Pyramid C Hexagonal Prism D Rectangular PyramidE Cylinder F Cone
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1 Name the figure.
A Rectangular Prism B Triangular Pyramid C Hexagonal Prism D Rectangular PyramidE Cylinder F Cone
[This object is a pull tab]
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D
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2 Name the figure.
A Rectangular Pyramid B Triangular Prism C Octagonal Prism D Circular Pyramid E Cylinder F Cone
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2 Name the figure.
A Rectangular Pyramid B Triangular Prism C Octagonal Prism D Circular Pyramid E Cylinder F Cone
[This object is a pull tab]
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E
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3 Name the figure.
A Rectangular Pyramid B Triangular Pyramid C Triangular Prism D Hexagonal Pyramid E Cylinder F Cone
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3 Name the figure.
A Rectangular Pyramid B Triangular Pyramid C Triangular Prism D Hexagonal Pyramid E Cylinder F Cone
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B
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4 Name the figure.
A Rectangular Prism B Triangular Prism C Square Prism D Rectangular Pyramid E Cylinder F Cone
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4 Name the figure.
A Rectangular Prism B Triangular Prism C Square Prism D Rectangular Pyramid E Cylinder F Cone
[This object is a pull tab]
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A
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5 Name the figure.
A Rectangular Prism B Triangular Pyramid C Circular Prism D Circular Pyramid E Cylinder F Cone
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5 Name the figure.
A Rectangular Prism B Triangular Pyramid C Circular Prism D Circular Pyramid E Cylinder F Cone
[This object is a pull tab]
Ans
wer
F
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For each figure, find the number of faces, vertices and edges.Can you figure out a relationship between the number of faces, vertices and edges of 3-Dimensional Figures?
Name Faces Vertices Edges
Cube 6 8 12
Rectangular Prism 6 8 12
Triangular Prism 5 6 9
Triangular Pyramid 4 4 6
Square Pyramid 5 5 8
Pentagonal Pyramid 6 6 10
Octagonal Prism 10 16 24
Mat
h Pr
actic
e
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Euler's Formula
F + V = E + 2
Euler's Formula is the number of edges plus 2 is equal to the sum of the faces and vertices.
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6 How many faces does a pentagonal prism have?
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6 How many faces does a pentagonal prism have?
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7
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7 How many edges does a rectangular pyramid have?
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7 How many edges does a rectangular pyramid have?
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8
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8 How many vertices does a triangular prism have?
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8 How many vertices does a triangular prism have?
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6
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9 How many faces does a hexagonal pyramid have?
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9 How many faces does a hexagonal pyramid have?
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7
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10 How many vertices does a triangular pyramid have?
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10 How many vertices does a triangular pyramid have?
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4
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Volume
Return toTable ofContents
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Label
- Units3 or cubic units
Volume
Volume
- The amount of space occupied by a 3-D Figure - The number of cubic units needed to FILL a 3-D Figure (layering)click to reveal
click to reveal
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Label
- Units3 or cubic units
Volume
Volume
- The amount of space occupied by a 3-D Figure - The number of cubic units needed to FILL a 3-D Figure (layering)click to reveal
click to reveal
[This object is a pull tab]
Mat
h Pr
actic
e MP.6: Attend to Precision.
Ask: What labels (or units) should we use with our answers?
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Volume Activity
Click the link below for the activity.
Lab #1: Volume Activity
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Volume Activity
Click the link below for the activity.
Lab #1: Volume Activity
[This object is a pull tab]
Teac
her N
otes The URL for the lab is:
http://njctl.org/courses/math/8th-grade-math/3d-geometry/volume-activity/
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Volume of Prisms & Cylinders
Return toTable ofContents
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Volume
Volume of Prisms & Cylinders:
Area of Base x Height, or V = Bh
Area Formulas:
Rectangle = lw or bh
Triangle = bh or 2 Circle = πr2
click to reveal
(bh) 1 2
click to reveal
click to reveal
click to reveal
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Find the Volume
5 m
8 m
2 m
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Find the Volume
5 m
8 m
2 m
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VOLUME: 2x 5 10 (Area of Base)x 8 (Height)80 m3
VOLUME:V = B hV = l w hV = 5 2 8V = 10 8V = 80 m3
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Find the Volume Use 3.14 as your value of π.
10 yd
9 yd
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Find the Volume Use 3.14 as your value of π.
10 yd
9 yd
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VOLUME: 9 x 9 81x 3.14 254.34 x 10 2543.4 yd3
VOLUME:V = B hV = r2 hV = 3.14 92 10V = 3.14 81 10V = 254.34 10V = 2543.4 yd3
(Are
a of B
ase)
(Height)
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A cylinder with a radius measuring 2 cm and a height of 5 cm is compared to a cylinder with a radius of 4 cm and a height of 5 cm. Amy says that the volume of the cylinder with a radius of 4 cm is double the volume of the cylinder with a radius of 2 cm. She used 3.14 as her value of π. Is she correct? Explain your reasoning.
Start by calculating the volume of both cylinders.
V = (3.14)(2)2(5)
V = 62.8 cm3
V = (3.14)(4)2(5)
V = 251.2 cm3
Answer the question.
No, Amy is not correct. If the radius of the cylinder doubles, the volume does not double. Instead it quadruples.
click click
click
Find the Volume
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A cylinder with a radius measuring 2 cm and a height of 5 cm is compared to a cylinder with a radius of 4 cm and a height of 5 cm. Amy says that the volume of the cylinder with a radius of 4 cm is double the volume of the cylinder with a radius of 2 cm. She used 3.14 as her value of π. Is she correct? Explain your reasoning.
Start by calculating the volume of both cylinders.
V = (3.14)(2)2(5)
V = 62.8 cm3
V = (3.14)(4)2(5)
V = 251.2 cm3
Answer the question.
No, Amy is not correct. If the radius of the cylinder doubles, the volume does not double. Instead it quadruples.
click click
click
Find the Volume
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Mat
h Pr
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MP.3 - Construct viable arguments & critique the reasoning of others.
After calculating the volume of both cylinders, ask:
What do you think about what Amy predicted?
Do you agree? Why or Why not?
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Teachers:
Use this Mathematical Practice Pull Tab for the next 9 SMART Response slides.
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Teachers:
Use this Mathematical Practice Pull Tab for the next 9 SMART Response slides.
[This object is a pull tab]
Mat
h Pr
actic
e
MP.5 - Use appropriate tools strategically.
Ask: Can you make a model to show that?
Would it help to create a diagram/draw a picture?
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4 in
11 Find the Volume.
7 in 1 5
1 in 1 2
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4 in
11 Find the Volume.
7 in 1 5
1 in 1 2
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VOLUME: 7.2 x 1.5 10.8 (Area of Base)x 4 (Height) 43.2 in3
VOLUME:V = B hV = 7.2(1.5)(4)V = 43.2 in3
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12 Find the volume of a rectangular prism with length 2 cm, width 3.3 cm and height 5.1 cm.
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12 Find the volume of a rectangular prism with length 2 cm, width 3.3 cm and height 5.1 cm.
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VOLUME:V = B hV =2(3.3)(5.1)V = (6.6)(5.1)V = 33.66 cm3
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13 Which is a possible length, width and height for a rectangular prism whose volume = 18 cm 3
A 1 x 2 x 18B 6 x 3 x 3C 2 x 3 x 3D 3 x 3 x 3
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13 Which is a possible length, width and height for a rectangular prism whose volume = 18 cm 3
A 1 x 2 x 18B 6 x 3 x 3C 2 x 3 x 3D 3 x 3 x 3
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C
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14 Find the volume.
21 ft
42 ft
50 ft47 ft
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14 Find the volume.
21 ft
42 ft
50 ft47 ft
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wer
V = Bh & B = bh of the triangle
V = (21)(42)(50)
V = (882)(50)
V = 441(50)V = 22,050 ft3
1 2
1 2 1 2
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15 A box-shaped refrigerator measures 12 by 10 by 7 on the outside. All six sides of the refrigerator are 1 unit thick. What is the inside volume of the refrigerator in cubic units?
HINT: You may want to draw a picture!
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15 A box-shaped refrigerator measures 12 by 10 by 7 on the outside. All six sides of the refrigerator are 1 unit thick. What is the inside volume of the refrigerator in cubic units?
HINT: You may want to draw a picture!
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wer
10 in.7 in.
12 in.
8 in. 5 in.
10 in.
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16 Find the volume. Use 3.14 as your value of π.
6 m
10 m
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16 Find the volume. Use 3.14 as your value of π.
6 m
10 m
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Ans
wer
d = 10 m, so r = 5 m
V = r2 hV = 3.14 52 6V = 3.14 25 6V = 78.5 6V = 471 m3
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17 Which circular glass holds more water?
Note: Use 3.14 as your value of π.
AGlass A having a 7.5 cm diameter and standing 12 cm high
BGlass B having a 4 cm radius and a height of 11.5 cm
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17 Which circular glass holds more water?
Note: Use 3.14 as your value of π.
AGlass A having a 7.5 cm diameter and standing 12 cm high
BGlass B having a 4 cm radius and a height of 11.5 cm
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Ans
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Glass Ad = 7.5, so r = 3.75V = B hV = r2 hV = 3.14 (3.75)2 12V = 3.14 14.0625 12V = 529.875 cm3 Glass B
V = B hV = r2 hV = 3.14 (4)2 11.5V = 3.14 16 11.5V = 577.76 cm3
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18 What is the volume of the largest cylinder that can be placed into a cube that measures 10 feet on an edge? Use 3.14 as your value of π.
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18 What is the volume of the largest cylinder that can be placed into a cube that measures 10 feet on an edge? Use 3.14 as your value of π.
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Ans
wer d = 10 ft, so r = 5 ft & h = 10 ft
V = π (52)(10)V = π(25)(10)V = 785 ft3
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19 A circular garden has a diameter of 20 feet andis surrounded by a concrete border that has a width of three feet and a depth of 6 inches. What is the volume of concrete in the path? Use 3.14 as your value of π.
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19 A circular garden has a diameter of 20 feet andis surrounded by a concrete border that has a width of three feet and a depth of 6 inches. What is the volume of concrete in the path? Use 3.14 as your value of π.
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Ans
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dinner = 20, so rinner = 10 ftrouter = 10 + 3 = 13 ftV = Bh = πr2hV = [π(132) - π(102)](0.5)V = (169π - 100π)(0.5)V = (216.66)(0.5)V = 108.33 ft3
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Sometimes, a question will ask you to "Leave your answer in terms of π". This means that you treat π like a variable & only do the arithmetic operations with the remaining numbers.
Ex: If a cylinder has a radius of 3 and a height of 4, then
Volume = π(3)2(4)
= π(9)(4)
= 36π units2
Let's try some more problems like this one.
Click here to return to cones & spheres.
Answer in Terms of π
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Leave your answer in terms of π.
10 yd
9 yd
Find the Volume
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Leave your answer in terms of π.
10 yd
9 yd
Find the Volume
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VOLUME:V = B hV = r2 hV = 92 10V = 81 10V = 810 yd3
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30 ft
15 ft
Leave your answer in terms of π.
Find the Volume
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30 ft
15 ft
Leave your answer in terms of π.
Find the Volume
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Ans
wer
d = 15, so r = 7.5VOLUME:V = B hV = r2 hV = (7.5)2 30V = 56.25 30V = 1687.5 ft3
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20 A cylinder has a radius of 7 and a height of 2. What is its volume? Leave your answer in terms of π.
A 14π units3
B 28π units3
C 49π units3
D 98π units3
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20 A cylinder has a radius of 7 and a height of 2. What is its volume? Leave your answer in terms of π.
A 14π units3
B 28π units3
C 49π units3
D 98π units3 [This object is a pull tab]
Ans
wer
V = BhV = (7)2 2V = 49 2V = 98 units3
ππ
π
D
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21 A cylinder has a diameter of 12 in. and a height of 12 in. What is its volume? Leave your answer in terms of π.
A 144π in3
B 432π in3
C 864π in3
D 1,728π in3
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21 A cylinder has a diameter of 12 in. and a height of 12 in. What is its volume? Leave your answer in terms of π.
A 144π in3
B 432π in3
C 864π in3
D 1,728π in3 [This object is a pull tab]
Ans
wer
d = 12 in., so r = 6 in.V = BhV = (6)2 12V = 36 12V = 432 in3
ππ
πB
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22 A cylinder has a diameter of 17 in. and a height of 5 in. What is its volume? Leave your answer in terms of π.
A 106.25π in3
B 361.25π in3
C 425π in3
D 1,228.25π in3
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22 A cylinder has a diameter of 17 in. and a height of 5 in. What is its volume? Leave your answer in terms of π.
A 106.25π in3
B 361.25π in3
C 425π in3
D 1,228.25π in3 [This object is a pull tab]
Ans
wer
d = 17 in., so r = 8.5 in.V = BhV = (8.5)2 5V = 72.25 5V = 361.25 in3
ππ
πB
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23 A circular pool has a diameter of 40 feet and is surrounded by a wooden deck that has a width of 4 feet and a depth of 6 inches. What is the volume of the wooden deck? Leave your answer in terms of π.
A 88π ft3
B 176π ft3
C 400π ft3
D 576π ft3
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23 A circular pool has a diameter of 40 feet and is surrounded by a wooden deck that has a width of 4 feet and a depth of 6 inches. What is the volume of the wooden deck? Leave your answer in terms of π.
A 88π ft3
B 176π ft3
C 400π ft3
D 576π ft3 [This object is a pull tab]
Ans
wer
pool: d = 40 ft, so r = 20 ftdeck: r = 20 + 4 = 24 ftV = ( (24)2 - (20)2)(0.5)V = (576 - 400 )0.5V = 176 (0.5) V = 88 ft3
ππ
π
ππ
π
A
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Volume of Pyramids, Cones & Spheres
Return toTable ofContents
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Demonstration comparing volume of Cones & Spheres with volume of
Cylinders
click to go to web site
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(Area of Base x Height) = Bh 1 3
1 3
A cone is 1/3 the volume of a cylinder with the same base area (B) and height (h).
Area of Base x Height3
Bh3=
Volume of a Cone
click to reveal
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V = 2/3 (Volume of Cylinder)
r2 h( )2/3 V=or
V = 4/3 r3ππ
Volume of a Sphere
A sphere is 2/3 the volume of a cylinder with the same base area (B) and height (h).
click to reveal
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V = 2/3 (Volume of Cylinder)
r2 h( )2/3 V=or
V = 4/3 r3ππ
Volume of a Sphere
A sphere is 2/3 the volume of a cylinder with the same base area (B) and height (h).
click to reveal
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Figu
re
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How much ice cream can a Friendly’s Waffle cone hold if it has a diameter of 6 in and its height is 10 in? Use 3.14 as your value of π.
(Just Ice Cream within Cone. Not on Top)Volume and Mass used in portion control. $$$
Volume
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How much ice cream can a Friendly’s Waffle cone hold if it has a diameter of 6 in and its height is 10 in? Use 3.14 as your value of π.
(Just Ice Cream within Cone. Not on Top)Volume and Mass used in portion control. $$$
Volume
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Ans
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&
Mat
h Pr
actic
e
V = (3.14)(32)(10)
V = 92.3 in3
1 3
Questions to address MP.1:What information are you given? What is this problem asking?
Questions to address MP.4:Write a number sentence to model this problem.What connections do you see?
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24 Find the volume. Use 3.14 as your value of π.
4 in
9 in
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24 Find the volume. Use 3.14 as your value of π.
4 in
9 in
[This object is a pull tab]
Ans
wer
V = Bh
V = (π42)(9)
V = (16π)(9)
V = 3(50.24)V = 150.72 in3
1 3 1 3 1 3
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25 Find the Volume. Use 3.14 as your value of π.
5 cm8 cm
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25 Find the Volume. Use 3.14 as your value of π.
5 cm8 cm
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Ans
wer
V = Bh
V = (π52)(8)
V = (25π)(8)
V = (200π)
V = 209 cm3
1 3 1 3 1 3 1 3
1 3
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V = πr3
V = (3.14)(5.5)3
V = 696.6 cm3
4 3 4 3
If the radius of a sphere is 5.5 cm, what is its volume? Use 3.14 as your value of π.
Click here
Volume
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26 What is the volume of a sphere with a radius of 8 ft? Use 3.14 as your value of π.
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26 What is the volume of a sphere with a radius of 8 ft? Use 3.14 as your value of π.
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Ans
wer V = πr3
V = (3.14)(8)3
V = 2,143.57 ft3
4 3 4 3
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27 What is the volume of a sphere with a diameter of 4.25 in? Use 3.14 as your value of π.
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27 What is the volume of a sphere with a diameter of 4.25 in? Use 3.14 as your value of π.
[This object is a pull tab]
Ans
wer
d = 4.25, so r = 2.125
V = πr3
V = (3.14)(2.125)3
V = 40.17 in3
4 3 4 3
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Similar to when we found the volume of a cylinder, with a cone and a sphere, you could be asked to "Leave your answer in terms of π".
Click here if you need to review that property.
Volume in Terms of π
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You are selling lemonade in conic cups (cups shaped like cones). How much lemonade will each customer get to drink? Leave your answer in terms of π.
8 cm
11 cm
Volume in Terms of π
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You are selling lemonade in conic cups (cups shaped like cones). How much lemonade will each customer get to drink? Leave your answer in terms of π.
8 cm
11 cm
Volume in Terms of π
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Ans
wer
d = 8 cm, so r = 4 cm
V = (4)2 (11)
V = (16)(11)
V = cm3 = 58.6 cm3
1 3 1 3
π
π
π176 3
π
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If the radius of a sphere is 6 cm, what is its volume? Leave your answer in terms of π.
Volume in Terms of π
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If the radius of a sphere is 6 cm, what is its volume? Leave your answer in terms of π.
Volume in Terms of π
[This object is a pull tab]
Ans
wer
V = (6)3
V = (216)
V = cm3
V = 288 cm3
4 3 4 3
π
π
π864 3
π
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28 Find the volume of the cone below. Leave your answer in terms of π.
A 12π in3
B 36π in3
C 48π in3
D 144π in3 4 in
9 in
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28 Find the volume of the cone below. Leave your answer in terms of π.
A 12π in3
B 36π in3
C 48π in3
D 144π in3 4 in
9 in
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Ans
wer
V = (4)2 (9)
V = (16)(9)
V = (16)(3)V = 48 in3
1 3 1 3
π
π
ππ
C
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29 Find the volume of the sphere that has a diameter of 18 cm. Leave your answer in terms of π.
A 729π cm3
B 972π cm3
C 5,832π cm3
D 7,776π cm3
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29 Find the volume of the sphere that has a diameter of 18 cm. Leave your answer in terms of π.
A 729π cm3
B 972π cm3
C 5,832π cm3
D 7,776π cm3
[This object is a pull tab]
Ans
wer
d = 18 cm, so r = 9 cm
V = (9)3
V = (729)
V =
V = 972 cm3
4 3 4 3
π
π
π
π2916 3
B
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30 Find the volume of the cone below. Leave your answer in terms of π.
A 49π in3
B 84π in3
C 147π in3
D 252π in3 7 in
12 in
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30 Find the volume of the cone below. Leave your answer in terms of π.
A 49π in3
B 84π in3
C 147π in3
D 252π in3 7 in
12 in
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Ans
wer
d = 7 in., so r = 3.5 in.
V = (3.5)2 (12)
V = (12.25)(12)
V = (12.25)(4)V = 49 in3
1 3 1 3
π
π
ππ
A
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31 Find the volume of a sphere that has a radius of 4.5 cm. Leave your answer in terms of π.
A 27π cm3
B 91.125π cm3
C 121.5π cm3
D 364.5π cm3
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31 Find the volume of a sphere that has a radius of 4.5 cm. Leave your answer in terms of π.
A 27π cm3
B 91.125π cm3
C 121.5π cm3
D 364.5π cm3 [This object is a pull tab]
Ans
wer
V = (4.5)3
V = (91.125)
V =
V = 121.5 cm3
4 3 4 3
π
π
π
π364.5 3
C
Slide 65 (Answer) / 97
32 A sphere with a radius measuring 9 cm is compared to a sphere with a radius of 18 cm. Jeff says that the volume of the sphere with a radius of 18 cm is double the volume of the sphere with a radius of 9 cm. Is he correct? Explain your reasoning. When you are done calculating your answer, type in the number "1".
Slide 66 / 97
32 A sphere with a radius measuring 9 cm is compared to a sphere with a radius of 18 cm. Jeff says that the volume of the sphere with a radius of 18 cm is double the volume of the sphere with a radius of 9 cm. Is he correct? Explain your reasoning. When you are done calculating your answer, type in the number "1".
[This object is a pull tab]
Ans
wer
V = (9)3
V = (729)
V =
V = 972 cm3
4 3 4 3
π
π
π
π2,916 3
V = (18)3
V = (5,832)
V =
V = 7,776 cm3
4 3 4 3
π
π
π
π23,328 3
7,776 is not double the volume of 972 . It's 8 times bigger.
ππ
Slide 66 (Answer) / 97
(Area of Base x Height) = Bh 1 3
1 3
Area of Base x Height3
Bh3=
Volume of a Pyramid
A pyramid is 1/3 the volume of a prism with the same base area (B) and height (h).
click to reveal
Slide 67 / 97
Pyramids are named by the shape of their base..
The volume is a pyramid is 1/3 the volume of a prism with the same base area(B) and height (h).
V = Bh13
=5 m
side length = 4 m
V = Bh
V = (4)(4)(5)
V = (80)
V = 26 m3
1 3 1 3 1 3
2 3
Click here
Pyramids
Slide 68 / 97
33 Find the Volume of a triangular pyramid with a base edge of 8 in, base height of 4 in and a pyramid height of 10 in.
8 in
10 in
4 in
Slide 69 / 97
33 Find the Volume of a triangular pyramid with a base edge of 8 in, base height of 4 in and a pyramid height of 10 in.
8 in
10 in
4 in
[This object is a pull tab]
Ans
wer
V = Bh
V = [ (4)(8)](10)
V = [ (32)](10)
V = (16)(10)
V = 53 in3
1 3 1 3 1 3
1 3
1 3
1 2 1 2
Slide 69 (Answer) / 97
34 Find the volume.
8 cm
7 cm
15.3 cm
Slide 70 / 97
34 Find the volume.
8 cm
7 cm
15.3 cm
[This object is a pull tab]
Ans
wer
V = Bh
V = (8)(7)(15.3)
V = (56)(15.3)
V = 285.6 cm3
1 3 1 3 1 3
Slide 70 (Answer) / 97
More Practice / Review
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Slide 71 / 97
35 Find the volume.
15 mm
8 mm
22 mm
Slide 72 / 97
35 Find the volume.
15 mm
8 mm
22 mm
[This object is a pull tab]
Ans
wer
V = Bh
V = (15)(8)(22)
V = 880 mm3
1 3 1 3
Slide 72 (Answer) / 97
36 Find the volume of a rectangular pyramid with a base length of 2.7 meters and a base width of 1.3 meters, and the height of the pyramid is 2.4 meters.
HINT: Drawing a diagram will help!
Slide 73 / 97
36 Find the volume of a rectangular pyramid with a base length of 2.7 meters and a base width of 1.3 meters, and the height of the pyramid is 2.4 meters.
HINT: Drawing a diagram will help!
[This object is a pull tab]
Ans
wer
V = Bh
V = (2.7)(1.3)(2.4)
V = 2.808 m3
1 3 1 3
Slide 73 (Answer) / 97
37 Find the volume of a square pyramid with base edge of 4 inches and pyramid height of 3 inches.
Slide 74 / 97
37 Find the volume of a square pyramid with base edge of 4 inches and pyramid height of 3 inches.
[This object is a pull tab]
Ans
wer
V = Bh
V = (42)(3)
V = 16 in3
1 3 1 3
Slide 74 (Answer) / 97
38 Find the Volume.
9 m9 m
12 m
11 m
6 m
Slide 75 / 97
38 Find the Volume.
9 m9 m
12 m
11 m
6 m[This object is a pull tab]
Ans
wer
V = Bh
V = [ (9)(6)](11)
V = (27)(11)
V = 99 m3
1 3 1 3
1 2
1 3
Slide 75 (Answer) / 97
39 Find the Volume. Use 3.14 as your value of π.
14 ft
21 ft
Slide 76 / 97
39 Find the Volume. Use 3.14 as your value of π.
14 ft
21 ft
[This object is a pull tab]
Ans
wer
V = Bh
V = π(72)(21)
V = (3.14)(49)(21)
V = 1,077.02 ft3
1 3 1 3 1 3
Slide 76 (Answer) / 97
40 Find the Volume. Use 3.14 as your value of π.
8 in
6.9 in
Slide 77 / 97
40 Find the Volume. Use 3.14 as your value of π.
8 in
6.9 in
[This object is a pull tab]
Ans
wer
V = Bh
V = π(42)(6.9)
V = (3.14)(16)(6.9)
V = 115.552 in3
1 3 1 3 1 3
Slide 77 (Answer) / 97
41 Find the Volume.
4 ft
7 ft
8 ft
9 ft
Slide 78 / 97
41 Find the Volume.
4 ft
7 ft
8 ft
9 ft
[This object is a pull tab]
Ans
wer V = Bh
V = 7(4) (8) 2V= 112 ft3
Slide 78 (Answer) / 97
42 A cone 20 cm in diameter and 14 cm high was used to fill a cubical planter, 25 cm per edge, with soil. How many full cones of soil were needed to fill the planter?
20 cm
14 cm
25 cm
Slide 79 / 97
42 A cone 20 cm in diameter and 14 cm high was used to fill a cubical planter, 25 cm per edge, with soil. How many full cones of soil were needed to fill the planter?
20 cm
14 cm
25 cm[This object is a pull tab]
Ans
wer
Cone Cube1/3(3.14)(102)(14) 253
1465.3 cm3 15625 cm3
15625/1465.3 # 10.7 about 11 cones
Slide 79 (Answer) / 97
43 Find the Volume.
7 in8 in
9 in
9 in
2 in
Slide 80 / 97
43 Find the Volume.
7 in8 in
9 in
9 in
2 in
[This object is a pull tab]
Ans
wer
V = BhV = 7(2) (8) 2V= 56 in3
Slide 80 (Answer) / 97
Name a 3-D Figure that is not a polyhedron.
Slide 81 / 97
Name a 3-D Figure that is not a polyhedron.
[This object is a pull tab]
Ans
wer possible answers
cylindercone
Slide 81 (Answer) / 97
Name a 3-D figure that has 6 rectangular faces.
Slide 82 / 97
Name a 3-D figure that has 6 rectangular faces.
[This object is a pull tab]
Ans
wer
rectangular prism
Slide 82 (Answer) / 97
44 Find the volume.
40 m
70 m
80 m
Slide 83 / 97
44 Find the volume.
40 m
70 m
80 m
[This object is a pull tab]
Ans
wer V = Bh
V = 80(40)(70)V = 224,000 m3
Slide 83 (Answer) / 97
45 The figure shows a right circular cylinder and a right circular cone. The cylinder and the cone have the same base and the same height.
Part A: What is the volume of the cone, in cubic feet?
From PARCC EOY sample test calculator #11
A 12π ft3
B 16π ft3
C 36π ft3
D 48π ft3
Slide 84 / 97
45 The figure shows a right circular cylinder and a right circular cone. The cylinder and the cone have the same base and the same height.
Part A: What is the volume of the cone, in cubic feet?
From PARCC EOY sample test calculator #11
A 12π ft3
B 16π ft3
C 36π ft3
D 48π ft3
[This object is a pull tab]
Ans
wer
V = (4)2 (3)
V = (16)(3)
V = (16)V = 16 ft3
1 3 1 3
π
π
ππ
B
Slide 84 (Answer) / 97
46 Part B: What is the ratio of the cone's volume to the cylinder's volume?
Slide 85 / 97
46 Part B: What is the ratio of the cone's volume to the cylinder's volume?
[This object is a pull tab]
Ans
wer
Cylinder: V = (4)2(3)V = (16)(3)V = 48 ft3
ππ
ππ
Cone:V = 16 ft3
Ratio = = 16π48π
1 3
Slide 85 (Answer) / 97
Glossary & Standards
Return toTable ofContents
Slide 86 / 97
Glossary & Standards
Return toTable ofContents
[This object is a pull tab]
Teac
her N
otes Vocabulary Words are bolded
in the presentation. The text box the word is in is then linked to the page at the end of the presentation with the word defined on it.
Slide 86 (Answer) / 97
tip
traffic cone
cone
pencil
ice cream
Back to
Instruction
curved
polyhedron
surface
Cone A polyhedron that has one circular base with a vertex opposite of it
and sides that are curved.
Slide 87 / 97
candles
pizza
Pringles
can
Back to
Instruction
curved
polyhedron
surface
Cylinder A polyhedron that has two congruent
circular bases which are parallel to one another and sides that are curved.
Slide 88 / 97
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Instruction
Edge
Line segment formed where 2 faces meet.
A triangular pyramid has 6
edges.
Slide 89 / 97
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Instruction
Euler's Formula
The number of edges plus 2 is equal to the sum of the faces and vertices.
E + 2 = F + V
E + 2= F + VE + 2 = 4 + 4
E + 2 = 8E = 6faces = 4
vertices = 4pyramid:
Slide 90 / 97
Back to
Instruction
Face
Flat surface of a polyhedron.
A triangular pyramid has 4 faces. (there is
one you can't see)
Slide 91 / 97
Back to
Instruction
Polyhedron
A 3-D figure whosefaces are all polygons.
Cubes
Prisms
Pyramids
Made of:
Faces
Edges
Vertices
Cylinders
Cones
Slide 92 / 97
Rectangular
PrismTriangular
Prism
Prism
Pentagonal
Back to
Instruction
Prism A polyhedron that has two congruent,
polygon bases which are parallel to one another, sides that are rectangular,
and named by the shape of their base.
Block of cheese
bodyof
pencil
juicebox
Slide 93 / 97
Pentagonal Pyramid
SquarePyramidTriangular
Pyramid
Back to
Instruction
Pyramid
A polyhedron that has one polygon base with a vertex opposite of it,sides that are triangular,
and named by the shape of its base.
Slide 94 / 97
Back to
Instruction
Vertex
Point where two or more straight lines/faces/edges meet.
A Corner.
A triangular pyramid has 4
vertices.
Slide 95 / 97
Back to
Instruction
Volume
The number of cubic units needed to fill a 3D figure (layering).
The amount of space occupied by a 3D figure.
Label: Units3
or cubic units
volume of prisms
and cylinders:
area of base x height
V = area of base x h V = 2m x 5m x 8m
V = 80m3
Slide 96 / 97
Standards for Mathematical Practices
Click on each standard to bring you to an example of how to meet
this standard within the unit.
MP8 Look for and express regularity in repeated reasoning.
MP1 Make sense of problems and persevere in solving them.
MP2 Reason abstractly and quantitatively.
MP3 Construct viable arguments and critique the reasoning of others.
MP4 Model with mathematics.
MP5 Use appropriate tools strategically.
MP6 Attend to precision.
MP7 Look for and make use of structure.
Slide 97 / 97