Question

The height of a cone is equal to the diameter of the base. What expression represents the volume of the cone, in cubic units?

Answer 1

By definition, the volume of a cone is given by:

`V = (1/3) * (\pi) * (r ^ 2) * (h)`
Where,
r: radius of the circular base
h: height of the cone
Let's define a variable:
x: diameter of the base
We have then that the radio is:

`r = x / 2`
The height is:

`h = x`
Substituting values:

`V = (1/3) * (\pi) * ((x / 2) ^ 2) * (x)`
Rewriting:

`V = (1/3) * (\pi) * (x ^ 2/4) * (x) V = (1/12) * (\pi) * (x ^ 3)`
Answer:
An expression that represents the volume of the cone, in cubic units is:

`V = (1/12) * (\pi) * (x ^ 3)`