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

Answer:

$V=\frac{1}{3}\pi h^3$

Step-by-step 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 = $\frac{2h}{2}=h$

It means radius of the cone is h.

Volume of cone is

$V=\frac{1}{3}\pi r^2h$

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

Substitute r=h in the above formula.

$V=\frac{1}{3}\pi (h)^2h$

$V=\frac{1}{3}\pi (h)^{2+1}$

$V=\frac{1}{3}\pi (h)^{3}$

Therefore, the volume of pile of sand is $V=\frac{1}{3}\pi h^3$.