6-6 Volume of Prisms and Cylinders

Course 3

Warm Up

Problem of the Day

Lesson Presentation

Warm UpMake a sketch of a closed book using two-point perspective.

Course 3

6-6 Volume of Prisms and Cylinders

Course 3

6-6 Volume of Prisms and Cylinders

Math

Warm UpMake a sketch of a closed book using two-point perspective.

Possible answer:

Problem of the Day

You are painting identical wooden cubes red and blue. Each cube must have 3 red faces and 3 blue faces. How many cubes can you paint that can be distinguished from one another? only 2

Course 3

6-6 Volume of Prisms and Cylinders

Learn to find the volume of prisms and cylinders.

Course 3

6-6 Volume of Prisms and Cylinders

Vocabulary

prismcylinder

Insert Lesson Title Here

Course 3

6-6 Volume of Prisms and Cylinders

Course 3

6-6 Volume of Prisms and Cylinders

A prism is a three-dimensional figure named for the shape of its bases. The two bases are congruent polygons. All of the other faces are parallelograms. A cylinder has two circular bases.

Course 3

6-6 Volume of Prisms and Cylinders

If all six faces of a rectangular prism are squares, it is a cube.

Remember!

Height

Triangular prism

Rectangular prism

Cylinder

Base

Height

Base

Height

Base

Course 3

6-6 Volume of Prisms and Cylinders

VOLUME OF PRISMS AND CYLINDERSWords Numbers Formula

Prism: The volume V of a prism is the area of the base B times the height h.

Cylinder: The volume of a cylinder is the area of the base B times the height h.

B = 2(5)= 10 units2

V = 10(3)

= 30 units3

B = (22)= 4 units2

V = (4)(6) = 24 75.4 units3

V = Bh

V = Bh

= (r2)h

Course 3

6-6 Volume of Prisms and Cylinders

Area is measured in square units. Volume is measured in cubic units.

Helpful Hint

Find the volume of each figure to the nearest tenth.

Additional Example 1A: Finding the Volume of Prisms and Cylinders

Course 3

6-6 Volume of Prisms and Cylinders

A. A rectangular prism with base 2 cm by 5 cm and height 3 cm.

= 30 cm3

B = 2 • 5 = 10 cm2

V = Bh

= 10 • 3

Area of base

Volume of a prism

Find the volume of the figure to the nearest tenth.

Course 3

6-6 Volume of Prisms and Cylinders

B. 4 in.

12 in.

= 192 602.9 in3

B = (42) = 16 in2

V = Bh

= 16 • 12

Additional Example 1B: Finding the Volume of Prisms and Cylinders

Area of base

Volume of a cylinder

Find the volume of the figure to the nearest tenth.

Course 3

6-6 Volume of Prisms and Cylinders

C.

5 ft

7 ft

6 ft

V = Bh

= 15 • 7

= 105 ft3

B = • 6 • 5 = 15 ft212

Additional Example 1C: Finding the Volume of Prisms and Cylinders

Area of base

Volume of a prism

Find the volume of the figure to the nearest tenth.

Course 3

6-6 Volume of Prisms and Cylinders

A. A rectangular prism with base 5 mm by 9 mm and height 6 mm.

= 270 mm3

B = 5 • 9 = 45 mm2

V = Bh

= 45 • 6

Area of base

Volume of prism

Try This: Example 1A

Find the volume of the figure to the nearest tenth.

Course 3

6-6 Volume of Prisms and Cylinders

B. 8 cm

15 cm

B = (82)

= 64 cm2

= (64)(15) = 960

3,014.4 cm3

Try This: Example 1B

Area of base

Volume of a cylinderV = Bh

Find the volume of the figure to the nearest tenth.

Course 3

6-6 Volume of Prisms and Cylinders

C.

10 ft

14 ft

12 ft

= 60 ft2

= 60(14)

= 840 ft3

Try This: Example 1C

Area of base

Volume of a prism

B = • 12 • 10 12

V = Bh

A juice box measures 3 in. by 2 in. by 4 in. Explain whether tripling the length, width, or height of the box would triple the amount of juice the box holds.

Additional Example 2A: Exploring the Effects of Changing Dimensions

Course 3

6-6 Volume of Prisms and Cylinders

The original box has a volume of 24 in3. You could triple the volume to 72 in3 by tripling any one of the dimensions. So tripling the length, width, or height would triple the amount of juice the box holds.

A juice can has a radius of 2 in. and a height of 5 in. Explain whether tripling the height of the can would have the same effect on the volume as tripling the radius.

Additional Example 2B: Exploring the Effects of Changing Dimensions

Course 3

6-6 Volume of Prisms and Cylinders

By tripling the height, you would triple the volume. By tripling the radius, you would increase the volume to nine times the original.

A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box.

Try This: Example 2A

Course 3

6-6 Volume of Prisms and Cylinders

Tripling the length would triple the volume.

V = (15)(3)(7) = 315 cm3

The original box has a volume of (5)(3)(7) = 105 cm3.

Course 3

6-6 Volume of Prisms and Cylinders

A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box.

Try This: Example 2A

The original box has a volume of (5)(3)(7) = 105 cm3.

Tripling the height would triple the volume.

V = (5)(3)(21) = 315 cm3

Course 3

6-6 Volume of Prisms and Cylinders

A box measures 5 in. by 3 in. by 7 in. Explain whether tripling the length, width, or height of the box would triple the volume of the box.

Try This: Example 2A

Tripling the width would triple the volume.

V = (5)(9)(7) = 315 cm3

The original box has a volume of (5)(3)(7) = 105 cm3.

Course 3

6-6 Volume of Prisms and Cylinders

By tripling the radius, you would increase the volume nine times.

A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume.

Try This: Example 2B

V = 36 • 3 = 108 cm3

The original cylinder has a volume of 4 • 3 = 12 cm3.

A cylinder measures 3 cm tall with a radius of 2 cm. Explain whether tripling the radius or height of the cylinder would triple the amount of volume.

Try This: Example 2B

Course 3

6-6 Volume of Prisms and Cylinders

Tripling the height would triple the volume.

V = 4 • 9 = 36 cm3

The original cylinder has a volume of 4 • 3 = 12 cm3.

A section of an airport runway is a rectangular prism measuring 2 feet thick, 100 feet wide, and 1.5 miles long. What is the volume of material that was needed to build the runway?

Additional Example 3: Construction Application

Course 3

6-6 Volume of Prisms and Cylinders

length = 1.5 mi = 1.5(5280) ft

= 7920 ft

height = 2 ft

= 1,584,000 ft3

The volume of material needed to build the runway was 1,584,000 ft3.

width = 100 ft

V = 7920 • 100 • 2 ft3

A cement truck has a capacity of 9 yards3 of concrete mix. How many truck loads of concrete to the nearest tenth would it take to pour a concrete slab 1 ft thick by 200 ft long by 100 ft wide?

Try This: Example 3

Course 3

6-6 Volume of Prisms and Cylinders

V = 20,000(1)

B = 200(100)

= 20,000 ft2

= 20,000 ft3

27 ft3 = 1 yd320,000 27

740.74 yd3

740.74 9

= 82.3 Truck loads

Additional Example 4: Finding the Volume of Composite Figures

Course 3

6-6 Volume of Prisms and Cylinders

Find the volume of the the barn.

Volume of barn

Volume of rectangular

prism

Volume of triangular

prism+=

= 30,000 + 10,000

V = (40)(50)(15) + (40)(10)(50)12

= 40,000 ft3

The volume is 40,000 ft3.

Try This: Example 4

Course 3

6-6 Volume of Prisms and Cylinders

Find the volume of the figure.

3 ft

4 ft

8 ft

5 ft

= (8)(3)(4) + (5)(8)(3)12

= 96 + 60

V = 156 ft3

Volume of barn

Volume of rectangula

r prism

Volume of triangular

prism+=

Lesson QuizFind the volume of each figure to the nearest tenth. Use 3.14 for .

306 in3942 in3

Insert Lesson Title Here

160.5 in3

No; the volume would be quadrupled because you have to use the square of the radius to find the volume.

Course 3

6-6 Volume of Prisms and Cylinders

10 in.

8.5 in.3 in.

12 in.12 in.

2 in.

15 in.10.7 in.

1. 3.2.

4. Explain whether doubling the radius of the cylinder above will double the volume.