Question

The height of a right circular cylinder is 10.5m. Three times the sum of the areas of its two circular faces is twice the area of the curved surface. Find the volume of the cylinder.

Answer 1

Height of cylinder(h) = 10.5 m.
Let r be the radius, then
Sum of areas of two circular faces = $2\pi r^2$
and curved surface area =$2\pi rh$
According to the condition,
$3\times 2\pi r^2=2\times 2\pi rh$
$3r=2h=2\times 10.5cm=21cm$
$\therefore r=\frac{21}{3}=7cm$
Now, volume of cylinder= $\pi r^{2}h$
$=\frac{22}{7}\times 7\times 7\times 10.5c{m}^3=1617c{m}^3$