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A spherical ball of lead 6 cm in radius is melted and recast into three spherical balls. The radii of two these balls are 3 cm and 4 cm. The radius of third sphere is

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a

4.5 cm

b

5 cm

c

6 cm

d

4 cm

answer is B.

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Detailed Solution

$\frac{4}{3} {πR}^{3} = ({πr}_{1}^{3} + {πr}_{2}^{3} + {πr}_{3}^{3}) \frac{4}{3} \Rightarrow R^{3} = r_{1}^{3} + r_{2}^{3} + r_{3}^{3} \Rightarrow 6^{3} = 3^{3} + 4^{3} + r_{3}^{3} \Rightarrow 216 = 27 + 64 + r_{3}^{3} \Rightarrow r_{3}^{3} = 125 \Rightarrow r_{3} = 5 cm$

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