Question:
Three solid spheres of radii 3, 4 and 5 cm respectively are melted and converted into a single solid sphere. Find the radius of this sphere.
Solution:
Let R be the radius of single solid sphere.
Therefore,
Volume of single solid sphere = volume of all three spheres
$\frac{4}{3} \pi R^{3}=\frac{4}{3} \pi r_{1}^{3}+\frac{4}{3} \pi r_{2}^{3}+\frac{4}{3} \pi r_{3}^{3}$
$R^{3}=\left(3^{3}+4^{3}+5^{3}\right)$
$R^{3}=27+64+125$
$R^{3}=216$
$R=\sqrt{216}$
$=6$
$R=6$
Hence, the radius of single solid sphere = 6 cm.