Question

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

Answer 1

Let r be the radius and h be the height of the cylinder, then
$2\pi rh=264$ ...(i)
and $\pi r^{2}h=924$ ...(ii)
Dividing (ii) by (i),
$\frac{\pi r^{2}h}{2\pi rh}=\frac{924}{264}\Rightarrow r=3.5\times 2\Rightarrow r=7.0cm=7cm$
Substracting the vlaue of r in (i),
$2\pi rh=264\Rightarrow 2\times \frac{22}{7}\times 7\times h=26444h=264\Rightarrow h=\frac{264}{44}=6$
Radius = 7cm and height = 6cm
Diameter= $7\times 2=14cm$
and height = 6cm