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Transparency 5. Click the mouse button or press the Space Bar to display the answers. Splash Screen. Example 5-5c. Objective. Find the volumes of prisms and cylinders. Prism Volume = Area of base height of figure. Cylinder Volume. Example 5-5c. Vocabulary. Volume. - PowerPoint PPT PresentationTRANSCRIPT
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Click the mouse button or press the Click the mouse button or press the Space Bar to display the answers.Space Bar to display the answers.
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Objective
Find the volumes of prisms and cylinders
Prism Volume = Area of base height of figure
Cylinder Volume
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Vocabulary
Volume
The number of cubic units needed to fill the space occupied by a solid
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Vocabulary
Cylinder
A solid whose bases are congruent, parallel circles, connected with a curved side
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Vocabulary
Complex solid
An object made up of more than one type of solid
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Example 1 Find the Volume of a Rectangular Prism
Example 2 Find the Volume of a Triangular Prism
Example 3 Find the Volumes of Cylinders
Example 4 Find the Volumes of Cylinders
Example 5 Find the Volume of a Complex Solid
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Find the volume of the prism.
The prism has a rectangular base
1/5
Volume = Area of base Height of prism
Remember: The top and base have the same dimensions on a prism
Replace formula for rectangle in “area of base”
V = (L W) Height of prism
Note: Area of base is in parenthesis because area must be figured first
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Find the volume of the prism.
Replace L with 7 in
1/5
Volume = Area of base Height of prism
V = (L W) Height of prism
V = (7 in
Replace W with 5 in
5 in)
Replace Height of prism with 11 in
11 in
Follow order of operations P E MD AS
Work inside parenthesis
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Find the volume of the prism.
Multiply 7 in 5 in
1/5
Volume = Area of base Height of prism
V = (L W) Height of prism
V = (7 in 5 in) 11 in
V = 35 in2 11 in Multiply 35 in2 5 in
V = 385 in3 Answer:
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Find the volume of the prism.
Answer: V = 120 in3
1/5
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Find the volume of the prism.
2/5
Volume = Area of base Height of prism
The prism has a triangular base
Note: The base does not have to be on the bottom
Replace formula for triangle in “area of base”
Volume = ( bh) Height of prism
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Find the volume of the prism.
2/5
Volume = Area of base Height of prism
Replace b with base of triangle which is 15 ft
Volume = ( bh) Height of prism
Volume = ( 15 ft
Replace h with height of triangle which is 9 ft
9 ft)
Replace height of prism with 4 ft
4 ft
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Find the volume of the prism.
2/5
Volume = Area of base Height of prism
Volume = ( bh) Height of prism
Volume = ( 15 ft 9 ft) 4 ft Follow order of operations P E MD ASWork inside parenthesis
Multiply 15 ft 9 ft
Volume = 67.5 ft2 4 ft
Multiply 67.5 ft2 4 ft
Volume = 270 ft3 Answer:
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Find the volume of the prism.
Answer: V = 45 ft3
2/5
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Find the volume of the cylinder.
3/5
Volume = Area of base Height of prism
The prism has a circle base
Replace formula for circle in “area of base”
Volume = ( r2) Height of prism
Replace r with 3 cm
Volume = ( [3 cm]2)
Note: Put 3 cm in enclosures because must square both number and unit of measure
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Find the volume of the cylinder.
3/5
Volume = Area of base Height of prism
Replace height of prism with 12 cm
Volume = ( r2) Height of prism
Volume = ( [3 cm]2) 12 cm
Follow order of operations P E MD AS
Work inside parenthesis that are inside the parenthesis!
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Find the volume of the cylinder.
3/5
Volume = Area of base Height of prism
Multiply 3 cm 3 cm
Volume = ( r2) Height of prism
Volume = ( [3 cm]2) 12 cm
Volume = ( 9 cm2) 12 cm
Multiply 9 cm2 Volume = 28.26 cm2 12 cm
Do not clear display on calculator
Multiply 28.26 cm2 12 cm
Volume = 339.29 cm3 Answer:
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Find the volume of the cylinder.
Answer: V = 169.56 in3
3/5
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Find the volume of the cylinder.
diameter of base, 18 yd; height, 25.4 yd
4/5
Volume = Area of base Height of prism
A cylinder has a circle base
Replace formula for circle in “area of base”
Volume = ( r2) Height of prism
Replace r with 9 yd
Remember: radius is half the diameter
Volume = ( [9 yd]2)
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Find the volume of the cylinder.
diameter of base, 18 yd; height, 25.4 yd
4/5
Volume = Area of base Height of prism
Volume = ( r2) Height of prism
Volume = ( [9 yd]2)
Replace height of prism with 25.4 yd
25.4 yd
Follow order of operations P E MD ASWork inside parenthesis that are inside the parenthesis!
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Find the volume of the cylinder.
diameter of base, 18 yd; height, 25.4 yd
4/5
Volume = Area of base Height of prism
Volume = ( r2) Height of prism
Volume = ( [9 yd]2) 25.4 yd Multiply 9 yd 9 yd
Volume = ( 81 yd2) 25.4 yd Multiply 81 yd2
Do not clear display on calculator
Multiply 254.34 yd2 25.4 yd
Volume = 254.34 yd2 25.4 yd
Volume = 6,460.24 yd3Answer:
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Find the volume of the cylinder.
diameter of base, 8 yd; height, 10 yd
Answer: V = 502.40 yd3
4/5
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TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.
Identify each shape
5/5
The big shape is a rectangular prism
The hole in the box is a cylinder
Find the area of each shape and subtract the cylinder from the rectangular prism
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TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.
5/5
Volume = Area of base Height of prism
Replace formula for circle in “area of base”
Rectangular Prism:
V = (L W) Height of prism
Replace L with 4 cm
V = (4 cm
Replace W with 3 cm
3 cm)
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TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.
5/5
Volume = Area of base Height of prism
Replace height of prism with 6 cm
Rectangular Prism:
V = (L W) Height of prism
V = (4 cm 3 cm) 6 cm
Follow order of operations P E MD AS
Work inside parenthesis
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TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.
5/5
Volume = Area of base Height of prism
Multiply 4 cm 3 cm
Rectangular Prism:
V = (L W) Height of prism
V = (4 cm 3 cm) 6 cm
V = 12 cm2 6 cm Multiply 12 cm2 6 cm
V = 72 in3
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TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.
5/5
Volume = Area of base Height of prism
Cylinder:
Replace formula for circle in “area of base”
Volume = ( r2) Height of prism
Replace r with 1 cm
Volume = ( [1 cm]2)
Replace height of prism with 3 cm
3 cm
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TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.
5/5
Volume = Area of base Height of prism
Cylinder:
Volume = ( r2) Height of prism
Volume = ( [1 cm]2) 3 cmFollow order of operations P E MD AS
Work inside parenthesis that are inside the parenthesis!
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TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.
5/5
Volume = Area of base Height of prism
Cylinder:
Volume = ( r2) Height of prism
Volume = ( [1 cm]2) 3 cm
Multiply 1 cm 1 cmVolume = ( 1 cm2) 3 cmMultiply 1 cm2 Volume = 3.14 cm2 3 cmDo not clear display on calculator
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TOYS A wooden block has a single hole drilled entirely through it. What is the volume of the block? Round to the nearest hundredth.
5/5
Volume = Area of base Height of prism
Cylinder:
Volume = ( r2) Height of prism
Volume = ( [1 cm]2) 3 cm
Volume = ( 1 cm2) 3 cm
Volume = 3.14 cm2 3 cm
Multiply 3.14 cm2 3 cm
Volume = 9.42 cm3
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Rectangular Prism Cylinder
Subtract the volume of cylinder from volume of prism
V = 62.58 cm3Answer:
5/5
V = 9.42 cm3 V = 72 in3
V = 72 in3 - 9.42 cm3
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HOBBIES A small wooden cube has been glued to a larger wooden block for a whittling project. What is the volume of the wood to be whittled?
Answer:
*
5/5
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Assignment
Lesson 7:5Volume of Prisms and
Cylinders4 - 23 All