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A solid piece of iron in the form of a cuboid of dimensions $49\ cm \times 33\ cm \times 24\ cm$, is moulded to form a solid sphere. Find the radius of the sphere.
Given: A solid piece of iron in the form of a cuboid of dimensions $49\ cm \times 33\ cm \times 24\ cm$, is moulded to form a solid sphere.
To do: To find the radius of the sphere.
Solution:
Here $l=49\ cm$, $b=33\ cm$ and $h=24\ cm$
Let $r$ be the radius of the sphere.
Volume of a Cuboid $=lbh=49\ cm \times 33\ cm \times 24\ cm$
Volume of a Sphere $=\frac{4}{3}\pi r^3$
$\Rightarrow$ Volume of Cuboid $=$ Volume of Sphere
$\Rightarrow 49\times 33\times 24=\frac{4}{3}\pi r^3$
$\Rightarrow r^3=9261$
$\Rightarrow r=21\ cm$
Thus, the radius of the sphere is $21\ cm$.
Updated on: 10-Oct-2022
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