Question

A right circular cylinder just encloses a sphere of radius $r$ (see figure). Find the
(i) surface area of the sphere,
(ii) curved surface area of the cylinder and (iii) ratio of the surfaces obtained in (i) and (ii).

Answer 1

(i) SA of sphere $=4\pi r^2$

(ii) Height $=r+r=2r$

radius $=r$

$\Rightarrow$Curved Surface Area$=2\pi rh=2\pi r\left(2r\right)=4\pi r^2$

(iii) Ratio $=\frac{4\pi r^2}{4\pi r^2}=\frac{1}{1}$ or $1:1$