Question

Metallic spheres of radii $6cm,8cm$ and $10cm$ respectively, are melted to form a single solid sphere. Find the radius (in cm) of the resulting sphere.

Answer 1

Volume of resulting sphere = sum of volume of smaller spheres.

$\frac{4}{3}\pi R^3=\frac{4}{3}\pi (6{)}^3+\frac{4}{3}\pi (8{)}^3+\frac{4}{3}\pi [10{]}^2$

$R^3=6^3+8^3+{10}^3=216+512+1000$

$R^3=1728$

$\Rightarrow R=12cm$

$\therefore$ The radius of the resulting sphere is 12 cm