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?

Answer 1

Answer:

$\frac{4}{3} \pi r^3$.

Step-by-step 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 $\frac{4}{3} \pi r^3$.

Hope this helps!