Question

Metallic spheres of radii 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

Let $r_1,r_2,r_3$ be the radius of the given 3 spheres & R be the radius of a single solid sphere.

Given :

$r_1=6cm,r_2=8cm,r_3=10cm$

Volume of first metallic sphere $\left(V_1\right)=\frac{4}{3}\pi (r_1{)}^3=\frac{4}{3}\pi (6{)}^3$

Volume of second metallic sphere $\left(V_2\right)=\frac{4}{3}\pi (r_2{)}^3=\frac{4}{3}\pi (8{)}^3$

Volume of third metallic sphere $\left(V_3\right)=\frac{4}{3}\pi (r_3{)}^3=\frac{4}{3}\pi (10{)}^3$

Volume of single solid sphere $\left(V\right)=\frac{4}{3}\pi R^3$

A .T.Q

Volume of 3 metallic spheres= volume of single solid sphere

$V_1+V_2+V_3=V\frac{4}{3}\pi (6{)}^3+\frac{4}{3}\pi (8{)}^3+\frac{4}{3}\pi (10{)}^3=\frac{4}{3}\pi R^3\frac{4}{3}\pi (6^3+8^3+{10}^3)=\frac{4}{3}\pi R^{3}216+512+1000=R^{3}1728=R^3(12\times 12\times 12)=R^3{12}^3=R^{3}R=12$

Hence, the radius of the resulting sphere = 12 cm