A solid rectangular block of metal 49 cm by 44 cm by 18 cm is mel… - Vidyadip

Question

A solid rectangular block of metal $49 cm$ by $44 cm$ by $18 cm$ is melted and formed into a solidsphere. Calculate the radius of the sphere.

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Answer

Volume of rectangular block $= 49 \times 44 \times 18 cm^3 = 38808 cm^3 … (1)$
Let r be the radius of sphere
$\therefore$ Volume $=\frac{4}{3} \pi r^3=\frac{4}{3} \times \frac{22}{7} \times r^3=\frac{88}{21} r^3 \ldots \ldots . .(2)$
From $(1)$ and $(2)$
$\frac{88}{21} r^3=38808 $
$ \Rightarrow r^3=38808 \times \frac{21}{88}=441 \times 21 $
$ \Rightarrow r^3=9261 $
$ \Rightarrow r=21 cm $
Radius of sphere $= 21 cm$

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