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Volumes of Prisms and CylindersPowerPoint Presentation

Volumes of Prisms and Cylinders

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Volumes of Prisms and Cylinders

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The area of the base B=w= 3 5 = 15.

Lesson 11-4

Additional Examples

Find the volume of the prism below.

V= BhUse the formula for volume.

= 15 • 5Substitute 15 for B and 5 for h.

= 75Simplify.

The volume of the rectangular prism is 75 in.3.

Use the Pythagorean Theorem to calculate the length of the other leg.

292 – 202 = 841 400 = 441 21

Lesson 11-4

Additional Examples

Find the volume of the prism below.

The prism is a right triangular prism with triangular bases.

The base of the triangular prism is a right triangle where one leg is the base and the other leg is the altitude.

1

2

1

2

The area B of the base is bh= (20)(21) = 210. Use the area of the base to find the volume of the prism.

Lesson 11-4

Additional Examples

(continued)

V= BhUse the formula for the volume of a prism.

= 210 •40Substitute.

= 8400Simplify.

The volume of the triangular prism is 8400 m3.

The formula for the volume of a cylinder is V= r 2h. The diagram shows h and d, but you must find r.

1

2

r= d = 8

V= r 2hUse the formula for the volume of a cylinder.

= • 82•9Substitute.

= 576Simplify.

The volume of the cylinder is 576 ft3.

Lesson 11-4

Additional Examples

Find the volume of the cylinder below. Leave your answer in terms of .

You can use three rectangular prisms to find the volume.

Lesson 11-4

Additional Examples

Find the volume of the composite space figure.

Each prism’s volume can be found using the formula V = Bh.

Lesson 11-4

Additional Examples

(continued)

Volume of prism I = Bh = (14 • 4) • 25 = 1400

Volume of prism II = Bh = (6 • 4) • 25 = 600

Volume of prism III = Bh = (6 • 4) • 25 = 600

Sum of the volumes = 1400 + 600 + 600 = 2600

The volume of the composite space figure is 2600 cm3.