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Volume of Prisms & Cylinders

Volume of Prisms & Cylinders. Section 11- 4. Volume . The space a figure occupies measured in cubic units (in 3 , ft 3 , cm 3 ). Cavalieri ’ s Principle. If two space figures have the same height & the same cross-sectional area at every level, then they have the same volume.

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Volume of Prisms & Cylinders

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  1. Volume of Prisms & Cylinders Section 11-4

  2. Volume • The space a figure occupies measured in cubic units (in3, ft3, cm3)

  3. Cavalieri’s Principle • If two space figures have the same height & the same cross-sectional area at every level, then they have the same volume.

  4. Volume of a Prism • You can find the volume of a right prism by multiplying the area of the base by the height. • By Cavalieri’s Principle, you can extend this idea to any prism. • V = Bh

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

  6. Use the Pythagorean Theorem to calculate the length of the other leg. 292 – 202 = 841  400 = 441  21 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.

  7. 12 12 The area B of the base is bh= (20)(21) = 210. Use the area of the base to find the volume of the prism. (continued) V= BhUse the formula for the volume of a prism. = 210 •40Substitute. = 8400Simplify. The volume of the triangular prism is 8400 m3.

  8. The formula for the volume of a cylinder is V= r 2h. The diagram shows h and d, but you must find r. 12 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. Find the volume of the cylinder below. Leave your answer in terms of .

  9. You can use three rectangular prisms to find the volume. Find the volume of the composite space figure. Each prism’s volume can be found using the formula V = Bh.

  10. (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.

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