Question

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

Answer 1

Since 3 sphere are melted to form are new

sphere.

volume of 3 old sphere = volume of new spheres

volume of new spheres=

vol.of 1 ${}^{st}$ spheres + vol.sphers + vol. of3${}^{rd}$ spheres

We have volume of a sphere $V=\frac{4}{3}\pi r^3$

$\Rightarrow \frac{4}{3}\pi r^3=\frac{4}{3}\pi r_1^3+\frac{4}{3}\pi r_2^2+\frac{4}{3}\pi r_3^3$

$\Rightarrow r^3=r_1^3+r_2^3+r_3^3$

$\Rightarrow r^3=6^3+8^3+{10}^3$

$\Rightarrow r^3=216+512+1000=1728$

$\Rightarrow r^3=\sqrt[3]{3(12{)}^3}=12$ cm .

Hence, radius of the resulting sphere.