Question

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The volume of a right cone is 3000/pie units. If its radius measures 15/pie units, find its
height.

Answer 1

`(9000)/(225\pi^2) =h`

Explanation:

`\sf The\:formula\;to\:find \:the\: volume\:of\:a\:cone \:is,\\V = (1)/(3) \pi r^2 h`

Given that,

r ⇒ radius ⇒ 15π

Volume ⇒ 3000π

Height ⇒ ?

Let us find the value of height.

`\sf V = (1)/(3) \pi r^2 h\\\\3000\pi =\pi *225\pi^2h\\\\3000\pi = (1)/(3)* \pi *225\pi^2 *h\\\\\ (3000\pi)/(\pi) = ((1)/(3)* \pi *225\pi^2)/(\pi) \\\\ 3000= (1)/(3) *225\pi^2 *h\\\\3000= (225\pi^2h)/(3)\\\\3000*3=225\pi^2h\\\\9000=225\pi^2h\\\\(9000)/(225\pi^2) =(225\pi^2h)/(225\pi^2) \\\\(9000)/(225\pi^2) =h`