Question

he 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?

Answer 1

For plato users is option A

Explanation:

A. V =
`\pi`r3

Answer 2

`\large\boxed{V=\pi r^3}`

Explanation:

The formula of a volume of a pyramid:

`V=(1)/(3)BH`

B - base area

H - height

Let r - radius of the cone.

We have H = 3r.

The base of the cone:
`B=\pi r^2`.

Substitute:

`V=(1)/(3)\pi(r^2)(3r)` cancel 3

`V=\pi r^3`