Find the number of spherical lead shots, each of diameter 6 cm that can be made from a solid cuboid of lead having dimensions $24\ cm\times22\ cm\times12\ cm$.
Given: An spherical lead shots, each of diameter 6 cm that can be made from a solid cuboid of lead having dimensions $24\ cm\times22\ cm\times12\ cm$.
To do: To find the number of lead shots made from the cuboid.
Solution:
$l=24 cm,\ b=22\ cm\ and\ h=12\ cm$
Volume of cuboid $=lbh=24\times22\times12=6336\ cm^{3}$
Volume of sphere lead shot $=\frac{4}{3}\pi r^{3}=\frac{4}{3}\times\frac{22}{7}\times3^{3}=113.14\ cm^{3}$
Let the number of lead shots be $n$.
Volume of cuboid $= n\times$ volume of sphere
$6336 = n\times113.14$
$n = 56$
Thus, $56$ lead shots can be made from the given cuboid.
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