Question

A right circular cylinder just encloses a sphere of radius r. Find ratio of the surface area of the sphere and curved surface area of the cylinder.

Answer 1

Given that the cylinder just encloses a sphere of radius $r$.

Hence, radius of the cylinder $=$ radius of the sphere $=r$

and height of the cylinder $=$ diameter of the sphere $=2r$

To find: Ratio of the surface area of sphere and curved surface area of cylinder.

We know that,

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

and C.S.A. of cylinder $=2\pi rh$

$\therefore$Required ratio $=\frac{4\pi r^2}{2\pi rh}$

$\Rightarrow \frac{4\pi r^2}{2\pi r\left(2r\right)}$ $[h=2r]$

$\Rightarrow \frac{4\pi r^2}{4\pi r^2}=\frac{1}{1}$

Hence, the ratio of the surface area of the sphere and the curved surface area of the cylinder is $1:1$.