Question

A cone of base radius 24 cm is cut by a plane parallel to its base exactly in the middle of its vertical height. If the vertical height of the cone is 14 cm, then volume of frustum is equal to

• A. $8964.5c{m}^3$
• B. $6908c{m}^3$
• C. $2380c{m}^3$
• D. $7392c{m}^3$

Answer 1

The correct option is D $7392c{m}^3$

Given: Radius of cone (R) = 24 cm

and, height of cone (H) = 14 cm

Let the radius of new cone formed be r.

Height of frustum (h) $=\frac{1}{2}\times 14=7cm$ (Given)

The upper part of cone is cut by a plane parallel to its base then the ratio of radius of cones is equal to the ratio of height of cones.



$\Rightarrow \frac{h}{H}=\frac{r}{R}$

$\Rightarrow \frac{7}{14}=\frac{r}{24}$

$\Rightarrow r=12cm$

$\therefore$ Volume of frustum $=\frac{1}{3}\pi h(R^2+r^2+rR)$

$=\frac{1}{3}\times \frac{22}{7}\times 7\times ({24}^2+{12}^2+12\times 24)$

$=\frac{22}{3}\times 1008=7392c{m}^3$

Hence, the correct answer is option (d).