Question

A pile of sand in the shape of a cone with a diameter that is twice the height. Express the volume v of sand as a function of the height h.

Answer 1

`V=(1)/(3)\pi h^3`

Explanation:

It is given that the shape of a pile of sand is conical.

Diameter of cone is twice the height.

Let height of cone be h.

Diameter of cone = 2h

Radius of the cone =
`(2h)/(2)=h`

It means radius of the cone is h.

Volume of cone is

`V=(1)/(3)\pi r^2h`

where, r is radius and h is height of the cone.

Substitute r=h in the above formula.

`V=(1)/(3)\pi (h)^2h`

`V=(1)/(3)\pi (h)^(2+1)`

`V=(1)/(3)\pi (h)^(3)`

Therefore, the volume of pile of sand is
`V=(1)/(3)\pi h^3`.