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EXAMPLE 4 PowerPoint PPT Presentation


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EXAMPLE 4. Find the volume of an oblique cylinder. Find the volume of the oblique cylinder. SOLUTION. Cavalieri’s Principle allows you to use Theorem 12.7 to find the volume of the oblique cylinder. V = π r 2 h. Formula for volume of a cylinder. = π(4 2 )(7). Substitute known values.

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EXAMPLE 4

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EXAMPLE 4

Find the volume of an oblique cylinder

Find the volume of the oblique cylinder.

SOLUTION

Cavalieri’s Principle allows you to use Theorem 12.7 to find the volume of the oblique cylinder.

V = π r2h

Formula for volume of a cylinder

= π(42)(7)

Substitute known values.

= 112π

Simplify.


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EXAMPLE 4

Find the volume of an oblique cylinder

≈351.86

Use a calculator.

The volume of the oblique cylinder is about 351.86cm3.


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EXAMPLE 5

Solve a real-world problem

SCULPTURE

The sculpture is made up of 13 beams. In centimeters, suppose the dimensions of each beam are 30 by 30 by 90. Find its volume.


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B = Area of large rectangle – 4 Area of small rectangle

= 90 510 – 4(30 90)

Solve a real-world problem

EXAMPLE 5

SOLUTION

The area of the base Bcan be found by subtracting the area of the small rectangles from the area of the large rectangle.

= 35,100 cm2


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Solve a real-world problem

EXAMPLE 5

Use the formula for the volume of a prism.

V = Bh

Formula for volume of a prism

= 35,100(30)

Substitute.

= 1,053,000 cm3

Simplify.

The volume of the sculpture is 1,053,000 cm3, or 1.053 m3.


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The volume of the oblique prism = area of triangle length

1

2

= (8)(5) 9

for Example 4 and 5

GUIDED PRACTICE

4. Find the volume of the oblique prism shown below.

SOLUTION

= 180

The volume of the oblique prism is 180m3


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for Example 4 and 5

GUIDED PRACTICE

5. Find the volume of the solid shown below.

SOLUTION

Vs= Volume of prism – Volume of rectangle.

Use the formula for the volume of a prism.

V = Bh

Formula for volume of a prism

= 43.3(6)

Substitute.

= 259.81 ft3

Simplify.


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for Example 4 and 5

GUIDED PRACTICE

Volume of rectangle

V = lwh

Formula for volume

= 3(3)(6)

Substitute.

= 54 ft3

Simplify.

Vs= Volume of prism – Volume of rectangle.

=258.81 – 54

=205.81 ft3


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