Question

A sphere and a cylinder have the same radius and height. The volume of the cylinder is 27 xft?

Which equation gives the volume of the sphere?

O v2 (277)

© V.2 (27)

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Answer 1

Volume of sphere =
`(2)/(3)(27\pi) ft^3`

Explanation:

We are given that

Radius of sphere=Radius of cylinder=r

Height of sphere=Height of cylinder=h

Height of sphere=h=Diameter of sphere=2r

Volume of cylinder=
`27\pi ft^3`

Volume of cylinder=
`\pi r^2 h`

Using the formula

Volume of cylinder=
`\pi r^2(2r)=2\pi r^3=27\pi`

Volume of sphere=
`(4)/(3)\pi r^3`

Using the formula

Volume of sphere=
`(2)/(3)* 2\pi r^3=(2)/(3)(27\pi)`

Hence, the volume of sphere =
`(2)/(3)(27\pi) ft^3`