Question

Suppose that a sphere with radius 5a has the same volume as a cylinder of radius 2a What is the height of the cylinder? Give your answer in terms of a. Use the formulas V= 4/pi r^3 and V=pi(r)^2h for the volumes of a sphere and cylinder respectively.

Answer 1

Answer:
`h = (125a)/(3)`

Explanation:

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

radius =
`5a`

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

radius =
`2a`

substituting the radius given and equating the two , we have :

`(4)/(3)\pi (5a)^(3) = \pi (a)^(2)h`

`\pi` is common to the two , this means that it cancels out , the equation then becomes :

`(4)/(3)(125a^(3)) = 4a^(2)h`

`a^(2)` is also common , then we have

`(4)/(3)(125a) = 4h`

multiply through by 3

`4(125a) = 12h`

divide through by 4

`125a = 3h`

divide through by 3

`h = (125a)/(3)`