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

Given: $3\times$ sum of areas of two circular faces $=2\times$ area of curved surface

Height of a right circular cylinder $=10.5m$

Let $r$ be that radius of the given right circular cylinder.

$3\times$ sum of areas of two circular faces $=2\times$ area of curved surface

$\Rightarrow 3\times 2\pi r^2=2\times 2\pi rh$ [$\because$ Area of circular face $=\pi r^2$ and area of curved surface $=2\pi rh$ ]

$\Rightarrow 6\pi r^2=4\pi rh$

$\Rightarrow 3r=2h$

$\Rightarrow 3r=2\times 10.5=21$

$\therefore r=\frac{21}{3}=7m$

Now Volume of cylinder $=\pi r^{2}h=\frac{22}{7}\times 7\times 7\times 10.5m^3$

$=1617m^3$