A spherical ball of radius 3 cm is melted and recast into three spherical balls.

Question:

A spherical ball of radius 3 cm is melted and recast into three spherical balls. The radii of two of these balls are 1.5 cm and 2 cm. Find the radius of the third ball.

Solution:

Radius of the original spherical ball = 3 cm
Suppose that the radius of third ball is r cm.
Then volume of the original spherical ball = volume of the three spherical balls

$\Rightarrow \frac{4}{3} \pi \times 3^{3}=\frac{4}{3} \pi \times 1.5^{3}+\frac{4}{3} \pi \times 2^{3}+\frac{4}{3} \pi \times r^{3}$

$\Rightarrow 27=3.375+8+r^{3}$

$\Rightarrow r^{3}=27-11.375=15.625$

$\Rightarrow r=2.5 \mathrm{~cm}$

∴ The radius of the third ball is 2.5 cm.

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