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A prism, a cylinder and cone are equivalent. If the bases of the prism, the cylinder...

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jessica44 | Student, Undergraduate | eNotes Newbie

Posted April 27, 2012 at 4:03 AM via web

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A prism, a cylinder and cone are equivalent. If the bases of the prism, the cylinder and the cone are equivalen

A prism, a cylinder and cone are equivalent. If the bases of the prism, the cylinder and the cone are equivalent,compare 

a) the heights of the prism and the cylinder___________________________
b) the heights of the prism and the cone ___________________________

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leedygood7 | High School Teacher | eNoter

Posted April 27, 2012 at 5:17 AM (Answer #1)

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First, it is necessary to know how to get the volumes of each figures.

Volume of prism can be measured by (area of the base) X (height)

Volume of cylinder can be measured by the same way,
 (area of the base) X (height).

Volume of cone is calculated in a bit different way, 

1/3 X (area of the base) X (height)

In the given condition, all three figures have the same area of the base and the volume. Let the area be represented by A. So, in the case of prism and the cylinder, 

A X (height of prism) = A X (height of cylinder)
Therefore, height of the prism equals the height of cylinder

In the second case of prism and the cone,
A X (height of prism) = 1/3 X A X (height of the cone)
Therefore, height of the cone would be three times the height of the  prism. 

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