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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?
Solution
Let the total number of bullets be x.
Radius of a spherical bullet = `4/2`= 2 cm
Now,
Volume of a spherical bullet = `4/3π xx (2)^3 = 4/3 xx 22/7 xx 8`
∴ Volume of x spherical bullets = `4/3 xx 22/7 xx 8 xx x "cm"^3`
Volume of the solid cube = (44)3 cm3
Clearly,
Volume of x spherical bullets = volume of the cube
`4/3 xx 22/7 xx 8 xx x` = 44 x 44 x 44
x = `(44 xx 44 xx 44 xx 7 xx 3)/(4 xx 22 xx 8)`
x = 2541
Hence, total number of spherical bullets are 2541.
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