Question

In figure shown a right circular cone of height $30cm$ a small cone is cut of from the top by a plane parallel to the base. If the volume of the small cone is$\frac{1}{27}$ of the volume of given cone.
Find at what height above the base is the section made.

Answer 1

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

So, volume of the big cone$=\frac{1}{3}\pi r^2\left(30\right)$

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

Given that,

$\frac{1}{27}\left(\frac{1}{3}\pi r^2\right(30\left)\right)=\frac{1}{3}\pi r^{2}h$

$\Rightarrow \frac{30}{27}=h$cm

$\therefore$ The height above the base of the section made is $(30-h)$cm

$\Rightarrow 30-\frac{30}{27}$

$\Rightarrow 28.89$cm

Height from base.