The height of the pyramid in the diagram is three times the radius of the cone.

Question

The base area of the pyramid is the same as the base area of the cone. What is the expression for the volume of the pyramid in terms of the radius r of the cone?

A. 

V =  r³

B. 

V =   r²

C. 

V = 2  r²

D. 

V =   r³

E. 

V = 3  r³

Answer 1

Hi Sarah!

In this question, we know that the base of the cone and that of the pyramid are the same, and that the height of the pyramid is 3r. From this information as well as the fact that the formula for a pyramid's volume is

V=(1/3)(b*h), we can solve for the volume.

The radius of the cone is r, so using the formula for the area of a circle we can deduce that the area of the cone's base is pi*r^2.

Now that we know the cone's base, which is also the pyramid's base, we can solve for the area of the pyramid by plugging in the value of the base.

V=(1/3)(pi*r^2)(3r)

V=(3/3)*pi*r^3

V=pi*r^3

The answer here is A