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

Due to given condition we can conclude:
H = 2D
where D is diameter of base and H height of cone

Volume of cone is calculated by:

V = B*H = r^2*pi*H

Now we need to express H in terms of r. H = 2D = 2*2*r because D = 2r
V = r^2*pi*4r = 4r^3*pi