Question

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

Answer 1

We have,

$R=8cm$

$h=14cm$

Let the other end radius be $r$.

Volume of the frustum cone $=\frac{5676}{3}c{m}^3$

We know that the volume of the frustum cone

$=\frac{1}{3}\pi (R^2+r^2+Rr)h$

So,

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

$22(64+r^2+8\times r)\times 2=5676$

$44\times (64+r^2+8\times r)=5676$

$64+r^2+8\times r=129$

$r^2+8r-65=0$

$(r+13)(r-5)=0$

$r=5,-13$

Since, $r$ can not be negative.

Hence, the radius of other end is $5cm$.