Question

The surface area of a sphere of radius $5cm$ is $5$ times the curved surface area of a cone of radius $4cm$. Find the volume of the cone.

Answer 1

Surface area of sphere$=4\pi r^2=4\pi \times 5\times 5=100\pi c{m}^2$

curved surface area of cone$=\pi rlc{m}^2=4\pi lc{m}^2$

$\therefore 100\pi =5\left(4\pi l\right)$

$\Rightarrow l=5$cm

Now $l^2=h^2+r^2$

$\Rightarrow 5^2=h^2+4^2$

$\Rightarrow h^2=9$

$\Rightarrow h=3$

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

$=\frac{1}{3}\times \frac{22}{7}\times 4\times 4\times 3$

$=\frac{35.2}{7}$

$=50.29c{m}^3$.