Question

The height of a cone is twice the radius of its base.

What expression represents the volume of the cone, in cubic units?
A. 2/3πx^3
B. 4/3πx^2
C. 2πx^3
D. 4πx^3

Answer 1

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

Explanation:

From the way the answers are presented, it can be seen that x refers to the radius of the base of the cone

radius:
`x`

and we are told that the height is twice the radius, so:

height:
`2x`

and now we use the formula to calculate the volume of a cone:

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

where
`V` is volume,
`r` is radius, and
`h` is the height. and
`\pi` is a constant

in this case

`r=x`

`h=2x`

so we substitute thisvalues in the formula for the volume:

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

Rearranging the terms

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

which is option A.