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.

Question

asked Apr 23, 2021 147k views

1 Answer

Erdomester · Answer 1 · 2021-04-29T10:41:42+0000

Answer:

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

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
$V=(1)/(3)\pi h^3$ .