Question

A solid sphere of diameter $42cm$ is melted and rects into a number of smaller identical cones, each of diameter $7cm$ and height $3cm$. Find the number of cones of formed.

Answer 1

Given diameter of sphere = 42 cm

radius = 21 cm

volume of sphere = $\frac{4}{3}\pi (21{)}^3$

now this sphere is melted & recent into number of cones

let 'n' be number of cone than radius of cone

=$\frac{7}{2}cm$ ; height of cone=3 cm

volume of sphere $=n\times$ volume of cone

$n=\frac{\frac{4}{3}\pi (\frac{21}{2}{)}^3}{\frac{1}{3}\pi (\frac{7}{2}{)}^2}\times 3$ =$\frac{4\times 21\times 21\times 21\times 4}{7\times 7\times 3}=48\times 21=1008.$

$\therefore$ 1008 cones can be formed.