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Question
How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each bullet being 4 cm in diameter?
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Solution
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
`x(4/3)pi (d/2)^3 = 8^3`
`x(4/3)(22/7)(4/2)^3 = (44)^3`
`x(4/3)(22/7)(2)^3 = 85184`
`x = ((85184)(3)(7))/((22)(4)(8))`
x =2541
Therefore, 2541 small bullets can be made from the given lead cube.
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