Question

A cone is divided into two parts by drawing a plane through the midpoint of the axis parallel to its base compare the volume of the two parts into which the plane divides the cone

Answer 1

Please see the attachment

Answer 2

The ratio of volume of small cone and the frustum generated will be 1 : 7.

Step-by-step explanation:

Let R and H are the base radius and height of the large cone respectively.

So, its volume is V =  $\frac{1}{3}\pi R^{2} H$

Now, the small cone that is generated after dividing the large cone will have height $\frac{H}{2}$ and radius $\frac{R}{2}$.

Therefore, its volume will be equal to v = $\frac{1}{3}\pi (\frac{R}{2} )^{2}(\frac{H}{2} ) = \frac{1}{8}[\frac{1}{3} \pi R^{2}H] = \frac{V}{8}$

So, the frustum so generated will have volume $(V - \frac{V}{8} ) = \frac{7V}{8}$.

Therefore, the ratio of the volume of small cone and the frustum generated will be $\frac{V}{8} : \frac{7V}{8} = 1 : 7$ (Answer)