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.

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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 = π(4 2 )(7) Substitute known values. = 112π Simplify. Formula for volume of a cylinder

EXAMPLE 4 Find the volume of an oblique cylinder ≈ Use a calculator. The volume of the oblique cylinder is about cm 3.

EXAMPLE 5 Solve a real-world problem SCULPTUREThe sculpture is made up of 13 beams. In centimeters, suppose the dimensions of each beam are 30 by 30 by 90. Find its volume.

EXAMPLE 5 Solve a real-world problem SOLUTION The area of the base B can be found by subtracting the area of the small rectangles from the area of the large rectangle. B = Area of large rectangle – 4 Area of small rectangle = – 4(30 90) = 35,100 cm 2

EXAMPLE 5 Solve a real-world problem Use the formula for the volume of a prism. V = Bh Formula for volume of a prism = 35,100(30) Substitute. = 1,053,000 cm 3 Simplify. The volume of the sculpture is 1,053,000 cm 3, or m 3.

GUIDED PRACTICE for Example 4 and 5 4. Find the volume of the oblique prism shown below. SOLUTION The volume of the oblique prism = area of triangle length = (8)(5) = 180 The volume of the oblique prism is 180m 3

GUIDED PRACTICE for Example 4 and 5 5. Find the volume of the solid shown below. SOLUTION Use the formula for the volume of a prism. V = Bh Formula for volume of a prism = 43.3(6) Substitute. = ft 3 Simplify. Vs = Volume of prism – Volume of rectangle.

GUIDED PRACTICE for Example 4 and 5 Volume of rectangle V = lwh Formula for volume = 3(3)(6) Substitute. = 54 ft 3 Simplify. Vs = Volume of prism – Volume of rectangle. = – 54 = ft 3