Question

A cone of height 10 cm and a radius of 10 cm is to be divided into two parts by cutting through the midpoint of the vertical axis. Then the volume of the conical part is:

• A. $\frac{1000}{3}\pi c{m}^3$
• B. $\frac{500}{3}\pi c{m}^3$
• C. $\frac{250}{3}\pi c{m}^3$
• D. $\frac{125}{3}\pi c{m}^3$

Answer 1

The correct option is D $\frac{125}{3}\pi c{m}^3$

Given that the $height$ and $radius$ of the cone is $10cm$ and $10cm$ respectively.

The height and radius of the cone that was divided into two parts by cutting through midpoint of the vertical axis would be half the radius and the height of the given cone.

Therefore, $r_{new}=5cm$ and $h_{new}=5cm$.

Then volume of divided cone =$\frac{1}{3}\pi r^{2}h=\frac{1}{3}\times (5{)}^2\times 5=\frac{1\times 25\times 5\pi }{3}=\frac{125\pi }{3}c{m}^3$