Question

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

Answer 1

Total surface of solid cylinder = 462 $c{m}^2$

Curved surface area = $\frac{1}{3}$ of total surface area

=$\frac{1}{3}\times 462=154c{m}^2$

Let r be the radius and h be height, then

2$\pi$ rh = 154 .........(i)

and 2 $\pi r^2$ = 462 - 154 = 308 $c{m}^2$ .........(ii)

$\Rightarrow r^2=\frac{308}{2\pi }=\frac{308\times 7}{2\times 22}=49=(7{)}^2$

$\therefore$ r = 7 cm

From (i), rh = $\frac{154}{2\pi }=\frac{154\times 7}{2\times 22}=\frac{49}{2}$

$\Rightarrow h=\frac{49}{2\times r}=\frac{49}{2\times 7}=\frac{7}{2}$

$\therefore$ Radius = 7 cm and height = $\frac{7}{2}$ cm