Question

some one please help me I've been stuck on this for a while
The height of the pyramid in the diagram is three times the radius of the cone. The base area of t

The height of the pyramid in the diagram is three times the radius of the cone. 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?
V = pi r to the third power
V = 1\3 pi r to the second power
V = 2pi r to the second power
V = 1\9 pi r to the third power
V = 3pi r to the third power
http://assets.openstudy.com/updates/attachments/52ed0a71e4b0a362a894d223-binks-1391266519824-geo1.png for the pic

Answer 1

The area of the base of the cone is
\[B= \pi \times radius ^{2}\]
so to calculate the volume of the pyramid we use the formula
\[V=\frac{ areaofthebase \times height }{ 3 }\]
replacing with height=3r and the area of the base B=pi r^2 we get
\[V=\frac{ \pi r ^{2}\times3r }{ 3 }=\pi r ^{3}\]
Alternative A

Answer 2

@Natriumhydrid okay thank you so much!