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Volume Formulas for Prisms and Cylinders: Examples and Applications

Learn and apply the formulas for calculating the volumes of prisms and cylinders with practical examples. Understand Cavalieri’s principle and how it relates to cylinders. Practice finding volumes of composite three-dimensional figures.

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Volume Formulas for Prisms and Cylinders: Examples and Applications

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  1. Objectives Learn and apply the formula for the volume of a prism. Learn and apply the formula for the volume of a cylinder.

  2. Example 1A: Finding Volumes of Prisms Find the volume of the prism. Round to the nearest tenth, if necessary.

  3. Example 1B: Finding Volumes of Prisms Find the volume of the right regular hexagonal prism. Round to the nearest tenth, if necessary.

  4. Example 1C Find the volume of a triangular prism with a height of 9 yd whose base is a right triangle with legs 7 yd and 5 yd long.

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

  6. Example 2A: Finding Volumes of Cylinders Find the volume of the cylinder. Give your answers in terms of  and rounded to the nearest tenth.

  7. Example 2B: Finding Volumes of Cylinders Find the volume ofa cylinder with base area 121 cm2 and a height equal to twice the radius. Give your answer in terms of  and rounded to the nearest tenth.

  8. Example 3: Finding Volumes of Composite Three-Dimensional Figures Find the volume of the composite figure. Round to the nearest tenth. The volume of the rectangular prism is: V = ℓwh = (8)(4)(5) = 160 cm3 The base area of the regular triangular prism is: The volume of the regular triangular prism is: The total volume of the figure is the sum of the volumes.

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