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
WBBSE
Class X
Mathematics
Sphere
04 Mark
2025
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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