Question

The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r?

A.
IR
V =
2
3
V=4
B.
Oc. v=1
V = 1/2
v=1
D.
3
.

Answer 1

`(4)/(3) \pi r^3`.

Explanation:

Let's say that the radius is r. The base diameter is two times the radius, or 2r.

Since the height is two times the diameter, the height is 2 * 2r = 4r.

The volume of a cone is 1/3 * h * pi * r^2. So, the volume of the cone is 1/3 * 4r * pi * r^2 = 1/3 * pi * 4r^3 = 4/3 * pi * r^3.

So, the volume of the cone is
`(4)/(3) \pi r^3`.

Hope this helps!