- 1 - Geometry Rules! Chapter 11 Notes

Notes #16: Surface Area and Volume of Rectangular Prisms and Cubes (Section 11.2, 11.4) A. Let’s Draw! Rectangular Prism: - draw a rectangle, this is the front face of your prism - draw a congruent rectangle again behind and to the right of the first - connect the appropriate corners (bottom right to bottom right, etc.)

Cube: (A rectangular prism with ________________ _______________) - draw a square, this is the front face of your prism - draw a congruent square again behind and to the right of the first - connect the appropriate corners (bottom right to bottom right, etc.)

B. Key Vocabulary Prism: A 3D solid with 2 parallel and congruent _____________ and ____________________ faces Base: Altitude: Lateral Faces: Lateral Edges:

- 2 -

Lateral Area of a Prism

LA = __________________________________

Surface Area of a Prism

_____________________________________

SA = LA + 2B

SA = (______________) + 2(____________)

Volume of a Prism

________________________________________

V = Bh V = (_____________)(_____________)

Surface Area of a Cube

SA = 6e2

Volume of a Cube

V = e3

- 3 - For #1-3, Complete the table referring to rectangular prisms:

1.) 2.) 3.) For #4-5, Complete the table referring to cubes with side length e:

4. 5. e 3 cm

SA 600 in2 V

4.) 5.)

1. 2. 3. l 5 cm 2 in 3 m w 4 cm 2 m h 3 cm 6 in

LA 40 m2 SA V 60 in3

- 4 - 6.) Consider a box with dimensions 2, 3, and 4ft. Draw this box:

a) Find its surface area

b) Triple each dimension of the box. Find the ratio of the old dimensions to the new dimensions.

c) Find the surface area of the new box. Find the ratio of the old surface area to the new surface area.

d) How does changing dimensions affect surface area?

- 5 - Notes #17: Surface Area and Volume of other Prisms (Section 11.2, 11.4) Let’s Draw! Prism with bases that are equilateral triangles

Prism with bases that are isosceles triangles

Prism with bases that are right triangles

Prism with bases that are isosceles trapezoids

Prism with bases that are regular hexagons

Prism with bases that are rhombuses

For #1-5, refer to the right prism shown: 1. The prism is called a right _______________ prism. 2. How many lateral faces are there? ______ How many bases? ____ 3. What kind of shape is each lateral face?______________________ 4. Name a lateral edge: ______ Name an altitude: ______ 5. If the bases are regular hexagons with edges 8m, find: a) Lateral Area b) Base Area c) Surface Area d) Volume

- 6 - For #6-10, refer to the right prism shown: 6. The prism is called a right _______________ prism. 7. How many lateral faces are there? ______ How many bases? ____ 8. What kind of shape is each lateral face?______________________ 9. Name a lateral edge: ______ Name an altitude: ______ 10. If the bases are isosceles trapezoids with legs 5m and bases 6 and 14 find: a) Lateral Area b) Base Area c) Surface Area d) Volume Find the lateral area, surface area, and volume of each prism: 11.)

- 7 - 12.) A right prism with a base of a regular hexagon with perimeter 12m, h = 5m 13.) Base is an isosceles triangle with base 12cm and legs 10cm, h = 5cm

- 8 - Complete each problem below: 14.) A triangular prism has base edges of 5, 6, and 7cm long. If the prism’s lateral area is 162cm2, what is the height of the prism? 15.) The base of a prism is a 30°-60°-90° triangle with the shortest leg length of 6in. The height of the prism is 2.4in. Find the volume of the prism.

- 9 - Notes #18 Surface Area and Volume of Cylinders (Section 11.2, 11.4) Cylinders: Let’s Draw: - Draw a squished circle (ellipse) - Draw a congruent ellipse above it - connect the right and left “sides” with straight lines Key Pieces Base: Altitude: radius:

Lateral Area of a Cylinder

__________________________________ LA = 2 rhπ

LA =(_______________________)(___________)

Surface Area of a Cylinder

_________________________________ SA = LA + 22 rπ

SA = (____________) + 2(_____________)

- 10 -

Volume of a Cylinder __________________________________

V = 2r hπ

V = (_____________)(_____________)

Sketch each cylinder. Then find its lateral area, surface area, and volume: 1. r = 6, h = 5 2. diameter = 10, h = 3 3. r = 2, h = 7 4. The volume of a cylinder is 27π . If r = h, find r.

- 11 - 5. The lateral area of a cylinder is 20π . If h = 5, find r. 6. A small cylinder has been cut out of the larger cylinder below. Find the volume of the remaining solid. Leave your answer in terms of π.

- 12 - Notes # 19: Surface Area and Volume of Square Pyramids and cones (Section 11.3, 11.5) Let’s Draw: - draw a rhombus (sleepy square) - mark its center - from the center, draw a height - connect all corners of the rhombus to the top this height

Key Vocab Vertex: Base: Altitude: Lateral Edges: Lateral Faces: Slant Height: (l)

Key Right Triangles

D

A

C

B

X

E

E

X F

E

F C

F

4

3

Lateral Area of a Pyramid

__________________________________________

Or

2plLA =

LA = (__________________)(_______________)

2

- 13 -

Surface Area of a Pyramid ________________________________

SA = LA + B

SA = (_______________) + (_____________)

4

3

Volume of a Pyramid

________________________________________

V = 3Bh

V = (_____________)(_____________) 3

For #1-6, refer to the regular square pyramid: 1. XF = 2. l = 3. Area of ∆EBC = 4. Lateral Area =

D

A

C

B

X

E

F

Base edge = 10cmHeight = 12cm

5. Surface Area = 6. Volume =

- 14 - For #7–8, Complete the table for regular square pyramids: (right triangles)

7. 8. height, h

3 6

slant height, l 5

base edge 16

lateral edge

lh

7.) 8.) Sketch each pyramid and find its lateral area, surface area, and volume: 9. base edge = 8, height = 3 10. base edge = 12, slant height = 10

- 15 - Cones Let’s Draw: - draw an ellipse (squished circle) - from its center, draw a height - draw two straight lines connecting the height to the ellipse Key Pieces base: altitude: radius: slant height: (l)

Lateral Area of a Cone

LA = rlπ

OR

LA = (_______________________)(___________) 2

Surface Area of a Cone

SA = LA + 2rπ

SA = (_______________) + (_____________)

- 16 - Volume of a Cone

V = 2

3r hπ

V = (_____________)(_____________)

3

Sketch each cone. Then find each value: 11. r = 3, h = 4 Slant height =_____ LA = _____ SA = _____ V = _____

12. diameter = 12, h = 8

Slant height =_____

LA = _____

SA = _____

V = _____

13. h = 4, l = 10 radius =_____ LA = _____ SA = _____ V = _____

- 17 - Notes #20: Surface Area and Volume of Spheres (Section 11.6) Areas and Volumes of Similar Solids (Section 11.7) Spheres

Surface Area of a Sphere

A = 24 rπ

Volume of a Sphere

V = 34

3rπ

Sketch each sphere. Then find the indicated values: 1. r = 6 2. diameter = 10 A = _______ A = _______ V = _______ V = _______

- 18 - 3. The area of a sphere is 64π . Find 4. The volume of a sphere is 32

3π . Find

the radius and volume of the sphere. The radius and area of the sphere. r = ________ r = ________ V = _________ A = ________ Use the given circumference to find the surface area of each sphere. Round your answer to the nearest whole number. 5. 12 C m=

6. 32 C yd=

A sphere has the volume given. Find its surface area to the nearest whole number. 7. 31200 V in= 8. 3600 ftV =

- 19 - Areas and Volumes of Similar Solids Similar Solids: Given the two similar solids, find: (a) the ratio of their side lengths (b) the scale factor (c) the ratio of their base areas (d) the ratio of their total volumes Complete: If the scale factor of two similar solids is a:b, then

• The ratio of corresponding lengths is ________ (examples of lengths: ) • The ratio of bases areas, lateral areas, or surface areas is ________ • The ratio of volumes is ________

Complete the table below for two similar solids: 9. 10. 11. 12.

Scale Factor 3:5

Ratio of base perimeters

Ratio of heights 2:1

Ratio of lateral areas 4:9

Ratio of surface areas

Ratio of volumes 27:64

- 20 - The surface areas of two similar figures are given. The volume of the larger figure is given. Find the volume of the smaller figure.

13.

2

2

3

25

36

216

SA in

SA in

V in

=

=

=

14.

2

2

3

72

98

686

SA ft

SA ft

V ft

=

=

=

The volumes of two similar figures are given. The surface area of the smaller figure is given. Find the surface area of the larger figure.

15.

3

3

2

8

125

4

V ft

V ft

SA ft

=

=

=

16.

3

3

2

125

1000

150

V cm

V cm

SA cm

=

=

=

- 21 - Day 21: Geometry: Chapter 11 Study Guide

Please include units with your answers and when appropriate, leave your answers in terms of π

Prisms: 1. Find the lateral area and surface area of a rectangular prism with base dimensions of 4ft by 5ft, and prism height of 6ft. 3. The base of a prism is an equilateral triangle with sides 6m. If the height of the prism is 10m, find the lateral area, surface area, and volume of the prism.

2. Find the volume of a rectangular prism with base dimensions of 2in by 7in and prism height of 5in. 4. The base of a prism is a regular hexagon with sides 4in. If the height of the prism is 8in, find the lateral area, surface area, and volume of the prism.

- 22 - 5. The total area of a cube is 150cm2. Find the length of an edge of the cube and its volume.

6. The base of a prism is an isosceles trapezoid with bases 9 and 19 and legs of 13cm. If the height of the prism is 10cm, find its lateral area, surface area, and volume.

Pyramids: (These are regular square pyramids) 7. If the height of a pyramid is 6ft and its slant height is 10ft, find the length of a base edge and the length of a lateral edge.

8. If the base edge of a pyramid is 14cm and its lateral edge is 25cm, find the slant height and height of the pyramid.

- 23 - 9. Find the lateral area, surface area, and volume of the square pyramid with base edge of 12 and height of 8. 11. Find the lateral area, surface area, and volume of the square pyramid with height of 12 and slant height of 13.

10. Find the lateral area, surface area, and volume of the square pyramid with base edge of 8 and slant height of 5. 12. A square pyramid has a base area of 64ft2 and a volume of 192 ft3. Find its height.

- 24 - Cylinders: 13. Find the lateral area, surface area, and volume of the cylinder with radius 3m and height 8m. 15. The volume of a cylinder is 50π in3. If the height is 2in, find the radius, the lateral area, and the surface area.

14. Find the lateral area, surface area, and volume of the cylinder with radius 3 2 cm and height 8cm. 16. The lateral area of a cylinder is 18π km2. If the height is 6km, find the radius, the surface area, and the volume.

Cones 17. Find the lateral area, surface area, and volume of the cone with radius 4cm and height 3cm.

18. Find the lateral area, surface area, and volume of the cone with radius 8m and slant height 17m.

- 25 - 19. Find the height, slant height, surface area, and volume of a cone with radius 5ft and lateral area of 65π ft2.

20. Find the height, slant height, lateral area and surface area of the cone with radius 6cm and volume 96π cm3.

Spheres 21. Find the area and volume of a sphere with radius 7m.

22. Find the area and volume of a sphere with diameter 12ft.

23. Find the radius and area of a sphere with volume 32

3π cm3.

24. Find the radius and area of a sphere with volume 3900 in .

- 26 - Ratio of Dimensions 25. The scale factor of two similar solids is 2:5. What is the ratio of: a) their corresponding sides? b) the perimeters of their bases? c) their lateral areas? d) their volumes?

26. The scale factor of two similar solids is 3:4. The base area of the larger solid is 48m2. Find the base area of the smaller solid.

27. The ratio of the base areas of two similar solids is 4:9. What is the ratio of: a) their corresponding sides? b) their surface areas? c) the perimeter of their bases? d) their volumes? Area Review 29. Find the area of a regular hexagon with apothem 3cm.

28. The ratio of the volumes of two similar solids is 1:8. What is the ratio of: a) their base perimeters? b) their lateral areas? c) their surface areas? 30. Find the area of a regular hexagon with perimeter of 48 m.