Question

If the volume and surface area of a sphere are numerically the same, then its radius is __________.

Answer 1

Let r be the radius of sphere.

Volume of the sphere = $\frac{4}{3}\mathrm{\pi }$r³ cu. units

Surface area of the sphere = 4$\mathrm{\pi }$r² sq. units

It is given that the volume and surface area of sphere are numerically same.

$\therefore \frac{4}{3}\mathrm{\pi }{r}^3=4\mathrm{\pi }{r}^2$

⇒ r = 3 units

Thus, the radius of sphere is 3 units.

If the volume and surface area of a sphere are numerically the same, then its radius is ___3 units___.