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Surface Area And Volume of Sphere — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsSurface Area And Volume of Sphere3 Marks
Question
How many spherical bullets can be made out of a solid cube of lead whose edge measures $44\ cm$, each bullet being 4cm in diameter?
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Answer

In the given problem, we have a lead cube which is remolded into small spherical bullets Here,
edge of the cube $(s) = 44\ cm$
Diameter of the small spherical bullets $(d) = 4\ cm$ Now,
let us take the number of small bullets be $x$ So,
the total volume of $x$ spherical bullets is equal to the volume of the lead cube.
Therefore, we get, Volume of the $x$ bullets = volume of the cube $\text{x}\Big(\frac{4}{3}\Big)\pi\Big(\frac{\text{d}}{2}\Big)^3=\text{s}^3$
$\text{x}\Big(\frac{4}{3}\Big)\Big(\frac{22}{7}\Big)\Big(\frac{4}{2}\Big)^3=(44)^3$
$\text{x}\Big(\frac{4}{3}\Big)\Big(\frac{22}{7}\Big)(2)^3=85184$
$\text{x}=\frac{(85184)(3)(7)}{(22)(4)(8)}$
$\text{x}=2541$
Therefore, $2541$ small bullets can be made from the given lead cube.

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