Question

A sphere is inscribed in a right circular cylinder of diameter d. The surface area of the sphere is

Answer 1

Hello there!

If a sphere is inscribed in a cylinder of diameter $d$, then the diameter of sphere = diameter of cylinder.

So, radius of sphere = $\frac{d}{2}$.

Surface area of sphere $=4\pi r^{2}$

$=4\pi \left(\frac{d}{2}\right)^{2}$

$=4\pi \frac{d^{2}}{4}$

$=\pi d^{2}$

Therefore, the surface area of the sphere is $\pi d^{2}$.