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?
V = r2
V = r3
V = r3
V = r2

Answer 1

The formula for the volume of a cone is \[V=\frac{ 1 }{ 3 }b h\]

But since the area of the base, b, is \[\pi r^2\]

Answer 2

We get the formula \[V=\frac{ 1 }{ 3 }[\pi r^2]h\]

Answer 3

You are told that the height of the cone is 2 times the base diameter.
The base diameter is 2r.

What is h=2 times the base diameter, 2r? h= ?

Substitute this result into the last volume formula above.