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Calculate Volume of Oblique Cylinder and Solid

Use formulas to find the volume of an oblique cylinder and a solid object, solving real-world problems. Convert units as necessary.

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Calculate Volume of Oblique Cylinder and Solid

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  1. 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.

  2. EXAMPLE 4 Find the volume of an oblique cylinder ≈351.86 Use a calculator. The volume of the oblique cylinder is about 351.86cm3.

  3. 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.

  4. 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

  5. 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.

  6. 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

  7. 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.

  8. 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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