How many spherical bullets can be made out of a solid cube of lead whose edge measures 44 cm, each being 4 cm in diameter.

Explanation

Given that,lost of spherical lead shots made out a soild cube of lead
`therefore` Number of spherical shots `= ("Volumeof a solid cube of lead")/("Volume of a spherical lead shot") `
Given that, diameter of a spherical lead shot i.e, sphere = 4 cm
`rArr" ""Radius of a spheical lead shot "(r)=(4)/(2)`
`r = 2cm " "[therefore "diameter " = 2xx "radius"]`
So Volume of a spherical lead shot i..e, sphere
`" "= (4)/(3) pi r^(3)`
`" "(4)/(3) xx (22)/(7) xx (2)^(3) `
`" "= (4 xx 22 xx 8)/(21) cm^(3)`
Now, sine edge of a solid cube (a) = 44 cm
so, volume of a soild `= (a)^(3) = (44)^(3) = 44 xx 44 cm^(3)`
From Eq. (i)
Number of spherical lead shots `= (44 xx 44 xx 44)/(4 xx 22 xx 8) xx 21`
`" " = 11 xx 21 xx 11 = 121 xx 21`
`" " =2541`
Hence, the required number of spherical lead shots is 2541.