Question

Three solid spheres of diameter $2cm,12cm$ and $16cm$ are melted and made into a single sphere. Find the radius of the new sphere ?

Answer 1

$r_1=2,r_2=12,r_3=16$

Spheres of radii $r_1,r_2,r_3$ are melted into a sphere of radius $r_0$

$\therefore \frac{4}{3}\pi r_1^3+\frac{4}{3}\pi r_2^3+\frac{4}{3}\pi r_3^3=\frac{4}{3}\pi r_0^3=>r_0^3=r_1^3+r_2^3+r_3^3=>r_0^3=2^3+{12}^3+{16}^3=>r_0=18$

Therefore, radius of the new sphere is $18$cm.