Question

The curved surface area of a cylindrical pillar is 264 $m^2$ and its volume is 924 $m^3$. Find the diameter and the height of the pillar.

Answer 1

Curved surface area of a pillar = 264 $m^2$ and volume = 924 $m^3$

Let r be the radius and h be height, then 2$\pi$rh = 264

$\Rightarrow \frac{2\times 22}{7}rh=264\Rightarrow rh=\frac{264\times 7}{2\times 22}$

$\therefore$ rh = 42 .........(i)

and $\pi r^2$ h = 924

$\Rightarrow \frac{22}{7}{r}^2$ h = 924

$\Rightarrow r^{2}h=\frac{924\times 7}{22}$

$\therefore r^2$ h = 294 ................(ii)

Dividing (ii) by (i), r=$\frac{294}{42}$ = 7 From (i) rh = 42

$\Rightarrow 7h=42\Rightarrow h=\frac{42}{7}=6$

$\therefore Diameter=2r=2\times$ 7 = 14 m and height = 6 m