Question

In a right circular cone the radius of its base is $6cm$ and its height is $14cm$. A cross section is made through the mid-point of the height parallel to the base. Find the volume of the lower portion?

Answer 1

Volume of cone $=\frac{1}{3}\pi r^{2}h$

Volume of lower part = volume of full cone - volume of upper cone

For full cone $r=6,h=14cm$

For upper cone $r_1=\frac{r}{2}=\frac{6}{2}=3cm$ & $h=7cm$

Volume of lower part $=\frac{1}{3}\pi r^{2}h-\frac{1}{3}\pi r_1^{2}h$

$=\frac{1}{3}\pi (r^{2}h-r_1^{2}h)$

$=\frac{1}{3}\times \frac{22}{7}(6^2\times 14-3^2\times 7)$

$=\frac{1}{3}\times \frac{22}{7}\times 7(36\times 2-9)=\frac{1}{3}\times \frac{22}{7}\times 7(72-9)=462c{m}^3$