Question

Find the total surface area of sphere whose volume is equal to the volume of the cone having the radius $12cm$ and height $6cm$.

Answer 1

Volume of sphere$=$volume of cone
$\therefore \frac{4}{3}\pi r^3=\frac{1}{3}\pi r^{2}h$
$\frac{4}{3}\times \frac{22}{7}\times r^3=\frac{1}{3}\times \frac{22}{7}\times 12\times 12\times 6$
$4r^3=12\times 12\times 6$
$r^3=\frac{12\times 12\times 6}{4}$
$\therefore r^3=216$
$\therefore r=\sqrt[3]{3216}$
$r=6cm$
Total surface area of a sphere $==4\pi r^2=4\times \frac{22}{7}\times 6\times 6$
T.S.A of a sphere $=452.57sq.cm$