Question

The height of a cone is twice the radius of its base. What expression represents the volume of the cone, in cubic units?

Answer 1

A.
`V = (2)/(3)\pi x^3`

Explanation:

Formula for volume of a cone:
`V = (1)/(3)\pi r^2h`, where we know r = x, and h = 2x.

We can substitute the variables in the formula to find the expression that represents the total volume of the cone.

`V = (1)/(3)\pi r^2h\\V = (1)/(3)\pi x^2*2x\\V = (1)/(3)\pi 2x^3`Which simplifies into:

A.
`V = (2)/(3)\pi x^3`

Answer 2

Explanation:

Radius = r units

Height = 2r

Volume of cone = (1/3)πr²h

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