Question

The slant height of a right circular cone is 10 cm and its height is 8 cm. It is cut by a plane parallelel to its base passing through midpoint of of the height. Find ratio of the volume of the cone to that of the frustum of the cone cut.

Answer 1

The ratio of volume of the cone to that of the frustum of the cone cut will be 8 : 7.

Step-by-step explanation:

The slant height is 10 cm and the height is 8 cm of a right circular cone.

So, the radius of the base of the cone will be $\sqrt{10^{2} - 8^{2}} = 6$ cm.

Now, the volume of the cone will be $\frac{1}{3} \pi r^{2} h = 96\pi$ cubic cm.

If we cut it by a plane parallel to its base passing through the midpoint of the height.

Then the upper small cone will have a base radius of 3 cm and height 4 cm.

So, its volume = $\frac{1}{3} \pi r^{2} h = 12\pi$ cubic cm.

Therefore, the ratio of the volume of the cone to that of the frustum of the cone cut will be 96π : (96π - 12π) = 8 : 7 (Answer)