Question:
The height of a right circular cylinder is 10.5 m. 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.
Solution:
Let, r be the radius of the right circular cylinder
h be the height of the right circular cylinder
h = 10.5 cm
$\Rightarrow 3\left(2 \pi r^{2}\right)=2(2 \pi r h)$
⟹ 3r = 2h
⟹ r = 2/3 ∗ h
⟹ r = 2/3 ∗ 10.5
⟹ r = 7cm
Volume of the cylinder $=r^{2}{ }^{*} h$
= 22/7 * 7 * 7 * 10.5
= 154 * 10.5
$=1617 \mathrm{~cm}^{3}$