Question

Solid spheres of radii $3cm,4cm$ and $5cm$ are melted to form a single sphere. Find the radius of the new sphere (in cm).

Answer 1

To find the radius,

Let radius of formed sphere be $r$

Volume of given spheres = volume of formed sphere

$\frac{4}{3}\pi (3{)}^3+$ $\frac{4}{3}\pi (4{)}^3+$ $\frac{4}{3}\pi (5{)}^3$$=\frac{4}{3}\pi (r{)}^3$

$⟹27c{m}^3+64c{m}^3+125c{m}^3=r^3$

$⟹216c{m}^3=r^3$

Hence , $r=6cm$