Question

The base area of a cone is $38.5$ cm${}^2$. Its volume is $77$ cm${}^3$. Find its height.

Answer 1

The base area of a cone is $38.5$ $c{m}^2$

Given: Volume $=77$ $c{m}^3$

The base area of the cone $=\pi$$r^2=38.5c{m}^2$

Volume of the cone $=\frac{1}{3}\pi$$r^{2}h$

$V=\frac{1}{3}\times \left(\pi r^2\right)\times h$

$\Rightarrow 38.5\times h\times \frac{1}{3}=77$

$\Rightarrow h=\frac{77}{38.5}\times 3$

$\Rightarrow h=6cm$

The height of the cone is $6$ $cm$