Question

A vessel is in the form of a frustum of a cone. Its radius at one end is $8cm$ and the height is $14cm$. If its volume is $\frac{5676}{3}c{m}^3$, find the radius of the other end.

Answer 1

$R=8cm,h=14cm$,
Volume of frustum $=\frac{5676}{3}{cm}^3$

$\Rightarrow \frac{1}{3}\pi h(R^2+r^2+R\times r)=\frac{5676}{3}$
$\Rightarrow \frac{22}{7}\times 14(8^2+r^2+8r)=5676$

$\Rightarrow 64+r^2+8r=\frac{5676}{44}=129$
$\Rightarrow r^2+8r+64-129=0$

$\Rightarrow r^2+8r-65=0$
$\Rightarrow r^2+13r-5r-65=0$
$\Rightarrow (r+13)(r-5)=0$

$\therefore$ $r=-13and5$, neglect negative value.

$\therefore$ $r=5$

Hence radius of other end is $5$ cm.