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Volume of Prisms and Cylinders

Volume of Prisms and Cylinders. The volume of a three-dimensional figure is the number of nonoverlapping unit cubes of a given size that will exactly fill the interior. OR Volume is how much cubic space a figure will hold. Example 1A: Finding Volumes of Prisms.

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Volume of Prisms and Cylinders

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  1. Volume of Prisms and Cylinders

  2. The volumeof a three-dimensional figure is the number of nonoverlapping unit cubes of a given size that will exactly fill the interior. OR Volume is how much cubic space a figure will hold

  3. Example 1A: Finding Volumes of Prisms Find the volume of the prism. Round to the nearest tenth, if necessary. V = ℓwh Volume of a right rectangular prism = (13)(3)(5) = 195 cm3 Substitute 13 for ℓ, 3 for w, and 5 for h.

  4. Example 1B: Finding Volumes of Prisms Find the volume of a cube with edge length 15 in. Round to the nearest tenth, if necessary. V = s3 Volume of a cube = (15)3 = 3375 in3 Substitute 15 for s.

  5. Example 2: Recreation Application A swimming pool is a rectangular prism. Estimate the volume of water in the pool.

  6. Example 2 Continued Find the volume of the swimming pool in cubic feet. V = ℓwh = (25)(15)(19) = 3375 ft3

  7. Check It Out! Example 2 What if…? Estimate the volume if the height were doubled. Find the volume of the aquarium in cubic feet. V = ℓwh = (120)(60)(16) = 115,200 ft3

  8. Cavalieri’s principle also relates to cylinders. The two stacks have the same number of CDs, so they have the same volume.

  9. Example 3A: Finding Volumes of Cylinders Find the volume of the cylinder. Give your answers in terms of  and rounded to the nearest tenth. V = r2h Volume of a cylinder = (9)2(14) = 1134 in3  3562.6 in3

  10. Check It Out! Example 3 Find the volume of a cylinder with a diameter of 16 in. and a height of 17 in. Keep your answer in terms of . V = r2h Volume of a cylinder = (8)2(17) Substitute 8 for r and 17 for h. = 1088 in3  3418.1 in3

  11. radius and height multiplied by : Example 4: Exploring Effects of Changing Dimensions The radius and height of the cylinder are multiplied by . Describe the effect on the volume. original dimensions:

  12. Notice that . If the radius and height are multiplied by , the volume is multiplied by , or . Example 4 Continued The radius and height of the cylinder are multiplied by . Describe the effect on the volume.

  13. Volume of Cones

  14. Example: Finding Volumes of Cones Find the volume of a cone with radius 7 cm and height 15 cm. Give your answers both in terms of  and rounded to the nearest tenth. Volume of a pyramid Substitute 7 for r and 15 for h. = 245 cm3 ≈ 769.7 cm3 Simplify.

  15. Check It Out! Example 3 Find the volume of the cone. Volume of a cone Substitute 9 for r and 8 for h. ≈ 216m3 ≈ 678.6 m3 Simplify.

  16. Homework Page 83, #3, 5 Page 85, #13 Page 86, #15, 17 Page 87, #20, 21, 26 Page 88, #29 Page 89, #37a, 38a

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