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?

Answer 1

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 × 44 × 44

x = `(44 xx 44 xx 44 xx 7 xx 3)/(4 xx 22 xx 8)`

x = 2541

Hence, the total number of spherical bullets is 2541.