Question

3 spheres of radii 3cm, 4cm, 5cm respectively are melted together to form a single solid sphere. Find the radius of the resulting sphere.

• A. 5.02 cm
• B. 2.21 cm
• C. 6.95 cm
• D. 6.22 cm

Answer 1

The correct option is A

5.02 cm

Let radius of the new sphere be r cm

Volume of a Sphere $=\frac{4}{3}\pi ({r_1}^3+{r_2}^3+{r_3}^3)=\frac{4}{3}\pi (3^3+4^3+5^3)=\frac{4}{3}\pi \left(198\right)c{m}^3$

Volume of the new sphere = $\frac{4}{3}\pi r^3$

Volume of the old solid = Volume of the new solid formed
$\frac{4}{3}\pi \left(198\right)=\frac{4}{3}\pi r^3$

Solving the equations with common terms on both sides, we get,
$r^3=198⟹r=5.02cm$