Question

A metallic right circular cone $20$cm high and whose vertical angle is ${60}^o$ is cut two parts at the middle of its height by a plane parallel to its base. If the frustum so obtained in drawn into a wire of diameter $1/16$cm, find the length of the wire.[Use $\pi =\frac{22}{7}$].

Answer 1

$\begin{array}{c}Volumeofcone\left(remaining\right)=Volumeofwire\\ \frac{1}{3}\pi {\left(20\right)}^2\\ \frac{1}{3}\pi {\left(\frac{20}{\sqrt{3}}\right)}^2\times 10-\frac{1}{3}\pi /{\left(\frac{10}{\sqrt{3}}\right)}^2\times 10\\ =\pi {\left(\frac{1}{32}\right)}^2\times l\\ \frac{4000}{27}-\frac{1000}{27}=\frac{l}{1024}\\ \frac{1000\times 1024}{9}=l\\ \left[l=1137.7m\right]\end{array}$