# The radius and the height of a right circular cone are in the ratio 5:12 and its volume is 2512 cubic cm. Find the radius and slant height of the cone . (Take pi = 3.14)?

Feb 22, 2018

let the radius be $5 x$ and the height be $12 x$.

Volume$= \pi {r}^{2} h$

$2512 = 3.14 \times 25 {x}^{2} \times 12 x$

$2512 = 942 {x}^{3}$

${x}^{3} = \frac{8}{3}$

$x = \frac{2}{\sqrt[3]{3}} = 1.39 c m$(approx)

So the radius would be. $5 x = 5 \times 1.39 = 6.95 c m$