Practice | Hashtable

1. If three metallic spheres of radii 6 cm, 8 cm and 10 cm are melted to from a single sphere, the diameter of the new sphere will be :

A. 12 cm

B. 24 cm

C. 30 cm

D. 36 cm

Solution:

Volume of new sphere :

\begin{aligned} = [\frac{4}{3} π \times {(6)}^{3} + \frac{4}{3} π \times {(8)}^{3} + \frac{4}{3} π \times {(10)}^{3}] c m^{3} \\ = [\frac{4}{3} π {{(6)}^{3} + {(8)}^{3} + {(10)}^{3}}] c m^{3} \\ = (\frac{4}{3} π \times 1728) c m^{3} \\ = [\frac{4}{3} π \times {(12)}^{3}] c m^{3} \end{aligned}

Let the radius of the new sphere be R
Then,

\begin{aligned} \frac{4}{3} π R^{3} = \frac{4}{3} π \times {(12)}^{3} \\ \Rightarrow R = 12 c m \end{aligned}

∴ Diameter :

\begin{aligned} = 2 R \\ = 2 \times 12 \\ = 24 c m \end{aligned}

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