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. The radius of the third ball is
(a) 1 cm
(b) 1.5 cm
(c) 2.5 cm
(d) 0.5 cm

 

Solution:

(c) 2.5 cm

Let cm be the radius of the third ball.
Volume of the original ball = volume of the three balls

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

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

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

 

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

 

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