Question

The radius and the height of right circular cone are in the ratio $5:12$ If its volume is $314$ cubic m. Find the diameter of its base $(\pi =31.4)$.

Answer 1

Let the radius and height be $5x$ and $12x$, respectively.

$\therefore$ Volume of the cone
$=\frac{1}{3}\times \left(3.14\right)\times {\left(5x\right)}^2\times \left(12x\right)$ $=314x^3$.

Given, volume $=314m^3$
Thus $314x^3=314$
$⟹$ $x^3=1$ $⟹$ $x=1$

Then, radius $=5\left(1\right)=5m$.

Therefore, Diameter $=2r=2\times 5=10m$.