Question
How many spherical bullets can be made out of a solid cube of lead whose edge measures 44cm, 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) = 44cm Diameter of the small spherical bullets (d) = 4cm 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.
$\text{x}\Big(\frac{4}{3}\Big)\Big(\frac{22}{7}\Big)\Big(\frac{4}{2}\Big)^3=(44)^3$
$\text{x}\Big(\frac{4}{3}\Big)\Big(\frac{22}{7}\Big)(2)^3=85184$
$\text{x}=\frac{(85184)(3)(7)}{(22)(4)(8)}$
$\text{x}=2541$
Therefore, 2541 small bullets can be made from the given lead cube.
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