Question

A spherical cannon ball 28 cm in diameter is melted and recast into a right circular conical mould, base of which is 35 cm in diameter. Find the height of the cone.

Answer 1

Sphere radius = $\frac{28}{2}=14cm$
volume of sphere = $\frac{4}{3}\pi r^3$
=$\frac{4}{3}\pi \times 14\times 14\times 14$
It is melted and recast to a conical shape
it's radius = $\frac{35}{2}=17.5cm$
= $\frac{1}{3}\pi \times r^2\times h$
= $\frac{1}{3}\pi \times 17.5\times 17.5\times h$
Now according to the question
volume of sphere =volume of cone
$\frac{4}{3}\pi \times 14\times 14\times 14=\frac{1}{3}\pi \times 17.5\times 17.5\times h$
$\frac{4}{3}\times 14\times 14\times 14=\frac{1}{3}\times 17.5\times 17.5\times h$
$3658.6=102.08\times h$
$\frac{3658.6}{102.08}=h$
$\therefore h=35.84cm$