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

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.