Question

A spherical ball of lead 3 cm in diameter is melted and recast into three spherical balls. If the diameters of two balls be $\frac{3}{2}$ cm and 2 cm, find the diameter of the third ball.

Answer 1

In the given problem, we have a spherical ball of lead which is remolded into 3 smaller balls.

Here, Diameter of the bigger ball (d) = 3 cm

Diameter of 1^st small ball (d₁) = cm

Diameter of 2^nd small ball (d₂) = cm

Let the diameter of the 3^rd ball = x cm.

So now,

Volume of the bigger ball = sum of the volumes of the smaller balls

Further, solving for x, we get

Further,

Therefore, the diameter of the third ball is.