Question

The total surface area of a cylinder is $462{cm}^2$ and its curved surface are is $\frac{1}{3}$ of its total surface area. Find the radius of the cylinder (in $cm$).

Answer 1

In cylinder
T.S.A $=462{cm}^2$
C.S.A $=\frac{1}{3}$ T.S.A
$r=?$
Now C.S.A$=\frac{1}{3}$ T.S.A
$2\pi rh=\frac{1}{3}\times 462$
$2\pi rh=154{cm}^2$
Now T.S.A $=$ C.S.A $+$ Area of bases
T.S.A $=2\pi rh+2\pi r^2$
$462=154+2\pi r^2$
$462-154=2\pi r^2$
$\Rightarrow$ $2\pi r^2=308$
$2\times \frac{22}{7}\times r^2=308$
$r^2=\frac{308\times 7}{2\times 22}$
$r^2=7\times 7$
$r^2=49$
$r=\sqrt{49}=7cm$
Radius of cylinder $=7cm$