Question

If a cone of radius $10cm$ is divided into two parts by drawing a plane through the mid-point of its axis, parallel to its base. Compare the volumes of the two parts.

Answer 1

Volume of cone$=\frac{1}{3}\pi r_1^2{h}_1=\frac{1}{3}\pi {\left(\frac{r}{2}\right)}^2\times \frac{h}{2}$

$=\frac{1}{3}\pi {\left(\frac{10}{2}\right)}^2\times \frac{h}{2}$

$=\frac{25\pi h}{6}c{m}^3$

Volume of frustum ABCD$=\frac{1}{3}\pi h_2(R^2+r^2+Rr)$

$=\frac{1}{3}\pi \times \frac{h}{2}({10}^2+5^2+10\times 5)$

$=\frac{175\pi h}{6}$

Required ratio$=\frac{\frac{25\pi h}{6}}{\frac{175\pi h}{6}}=\frac{25}{175}=\frac{1}{7}=1:7$