Question

A right circular cylinder has its height equal to two times its radius. It is inscribed in a right circular cone having its diameter equal to 10 cm and height 12 cm, and the axes of both the cylinder and the cone coincide. Then, the volume (in = $c{m}_3$ ) of the cylinder is approximately

• A. $107.5$
• B. $118.6$
• C. $127.5$
• D. $128.7$

Answer 1

Answer: (C)

$127.5$

Let the diameter of cylinder be $2r$.

Examining the cross section of the cone and cylinder, we find two similar triangles.

So, $\frac{12-2r}{12}=\frac{2r}{10}$ $⟹r=\frac{30}{11}$

$\therefore$ Volume of a cylinder $=\pi r^{2}h=\pi r^2\left(2r\right)$

$=2\times \frac{22}{7}\times \frac{(30{)}^2}{(11{)}^2}\times \frac{30}{11}=127.50$

Hence, option C is correct.