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

Answer 1

(c) 2.5 cm

Let r cm be the radius of the third ball.
Volume of the original ball = volume of the three balls
$$\begin{gathered} \frac{4}{3}\mathrm{\pi }\times 3^3=\frac{4}{3}\mathrm{\pi }\times 1.5^3+\frac{4}{3}\mathrm{\pi }\times 2^3+\frac{4}{3}\mathrm{\pi }{r}^3 \\ \Rightarrow 27=3.375+8+{\mathrm{r}}^3 \\ \Rightarrow r^3=27-11.375=15.625 \\ \Rightarrow r=2.5\mathrm{cm} \end{gathered}$$