Question

The height of sand in a cylindrical shaped can drops 3 inches when 1 cubic foot of sand is poured out. What is the diameter, in inches, of the cylinder?

Options

• \[\frac{24}{\pi}\]

   

• \[\frac{48}{\pi}\]

   

• \[\frac{32}{\pi}\]

   

• \[\frac{48}{\pi}\]

   

Answer 1

Let r be the radius of the cylinder. It is given that the height drops 3 inches, when 1 cubic foot of sand is poured out and 1 foot = 12 inch

So,

`12xx12xx12 = pi r^2 h`

`⇒ 12 xx 12 xx 12 = pi r^2 xx 3`

`⇒  r^2 = (12 xx 12 xx 4)/pi`

`⇒ r = 24/sqrt(pi)`

`⇒ 2r = 48/sqrt(pi)`