Question

Three solid spheres, whose radii are 3 cm, 4 cm and 5 cm melted into a single sphere, its radius is

• A. None of these
• B. 9 cm
• C. 6 cm
• D. 8 cm

Hint:

When melting multiple solid objects into a new object, use the volume formula for spheres and conserve the total volume.

Answer 1

The Correct Option is C

The volume of a sphere is given by: \[ V = \frac{4}{3} \pi r^3 \] The total volume of the three spheres is: \[ V_{\text{total}} = \frac{4}{3} \pi (3^3 + 4^3 + 5^3) = \frac{4}{3} \pi (27 + 64 + 125) = \frac{4}{3} \pi (216) \] The volume of the new sphere is: \[ V_{\text{new}} = \frac{4}{3} \pi r^3 \] Equating the total volume and solving for \(r\): \[ r^3 = \frac{216}{\frac{4}{3} \pi} \quad \Rightarrow \quad r = 6 \, \text{cm} \] Thus, the correct answer is 6 cm.