Question

how many spherical pellets of diameter 4 cm can be made out of a cube of lead for which each edge measures 27 cm ? round the answer to the whole number

Answer 1

587

Explanation:

A lead cube of side
`27\text{ cm}` is used to make spherical pellets of diameter
`4\text{ cm}`.

As the volume of lead is conserved, the volume of raw material equals the volume of finished products.

`\text{Volume of cube} = \text{Volume of spheres produced}`

Let us assume that
`n` cubes are produced. Volume of a cube of side
`s` is
`s^(3)`. The volume of a sphere of diameter
`d` is
`(\pi d^(3))/(6)`.

`(27\text{ cm})^(3)=n* ((\pi (4 cm)^(3))/(6) )\\\\19683\text{ cm}^(3)=n* (\frac{32\pi \text{ cm}^(3)}{3} )\\\\n=587.37`

n is rounded off to 587.

∴ 587 spherical pellets can be made.