Question

Three 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 C $6cm$

Let radius of the new sphere be $rcm$

Volume of combined spheres $=\frac{4}{3}\pi ({r_1}^3+{r_2}^3+{r_3}^3)=\frac{4}{3}\pi (3^3+4^3+5^3)=\frac{4}{3}\pi \left(216\right)c{m}^3$

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

Volume of the old solid = Volume of the new solid formed
$\frac{4}{3}\pi \left(216\right)=\frac{4}{3}\pi r^3$

Solving the equations with common terms on both sides, we get,
$⟹r^3=216⟹r=6cm$