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.
✓
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 $= 21 \ cm$
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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