Question

A solid cylinder has total surface area of $462c{m}^2$. Its curved surface area is one-third of its total surface are. Find the radius of the cylinder.

Answer 1

We have,
Curved surface area $=\frac{1}{3}\times$ Total surface area

$\Rightarrow 2\pi rh=\frac{1}{3}\times (2\pi rh+2\pi r^2)$

$\Rightarrow 4\pi rh=2\pi r^2$

$\Rightarrow 2h=r\dots \left(1\right)$

Now, Total surface area$=462$

$\Rightarrow$ Curved surface area$=\frac{1}{3}\times 462$

$\Rightarrow 2\pi rh=154$

$\Rightarrow 2\times \frac{22}{7}\times 2h^2=154$

$\Rightarrow h^2=\frac{154\times 7}{2\times 22\times 2}=\frac{49}{4}$

$\Rightarrow h=\frac{7}{2}$cm.

From $\left(1\right)$, $r=7$