Question

A spherical canon ball, $28$ cm in diameter is melted and cast into a right circular conical mould, the base of which is $35$ cm in diameter. Find the height of the cone, correct to one place of decimal.

Answer 1

$\begin{array}{c}Wehave\\ diameterofsphere=28cm\\ \therefore Radiusofsphere=\frac{28}{2}=14cm\\ Now,\\ volumeofsphere=\frac{4}{3}\pi r^3\\ =\frac{4}{3}\pi {\left(14\right)}^3\\ Now,itsmeltedandrecasttoaconiclshape\\ i{t}^{\prime }sradius=\frac{35}{2}=17.5cm\\ volumeofcone=\frac{1}{3}\pi r^{2}h\\ =\frac{1}{3}\pi {\left(17.5\right)}^{2}h\\ accordingtoquestion\\ volumeofsphere=volumeofcone\\ \Rightarrow \frac{4}{3}\pi {\left(14\right)}^3=\frac{1}{3}\pi {\left(17.5\right)}^{2}h\\ \Rightarrow \frac{4}{3}\times 14\times 14\times 14=\frac{1}{3}\times 17.5\times 17.5\times h\\ \Rightarrow 3658.6=102.08\times h\\ \Rightarrow h=\frac{3658.6}{102.08}\\ \therefore h=35.8\\ Hence,\\ Heightofconeis35.8cm.\end{array}$