WBBSEClass XMathematicsSphere04 Mark2025 Moderate

QQuestion

Melting a solid Lead sphere of diameter 12 cm, three small solid spheres are made. If the ratio of the diameter of the small spheres is 3 : 4 : 5 then find the radius of each small sphere

Exam-ready answer 04 Mark

Answer

Radius of Lead sphere (R) = \frac{12}{2} = 6 cm

Volume of Lead Sphere (V) = \frac{4}{3} × π × (6)³

Let the diameters of the three small spheres be 3x, 4x, 5x.

⇒ Radius of small spheres = 3x, 4x, 5x

Total volume of spheres = V1 + V2 + V3

\frac{4}{3} × π × (6)³ = \frac{4}{3} × π × (3x)³ + \frac{4}{3} × π × (4x)³ + \frac{4}{3} × π × (5x)³

\frac{4}{3} × π × (6)³ = \frac{4}{3} × π × (27x³ + 64x³ + 125x³)

⇒ 216 = 216x³

⇒ x = 1

∴ Radius of small spheres = 3 cm, 4 cm and 5 cm

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