Question

A solid metallic sphere of radius $10.5cm$ is melted and recast into a number of smaller cones, of each of radius $3.5cm$ and height $3cm$. Find the number o cone of formed.

Answer 1

solid sphere radius $=10.5cm$

cone radius $=3.5cm$

cone height $=3cm$

$\to$ volume of sphere $=no.ofcone\times volumeofeachcone$

$\therefore \frac{4}{3}\pi r^3=n\times \frac{1}{3}\pi R^2.h$

$\therefore 4\times (10.5{)}^3=n\times (3.5{)}^2\times 3$

$\therefore n=\frac{4\times (10.5{)}^3}{(3.5{)}^2\times 3}$

$\therefore n=126$

$\to$ no. of cone is $126$