By definition, the volume of a cone is given by:
[tex]V = (1/3) * (\pi) * (r ^ 2) * (h)
[/tex]
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:
[tex] r = x / 2
[/tex]
The height is:
[tex] h = x
[/tex]
Substituting values:
[tex]V = (1/3) * (\pi) * ((x / 2) ^ 2) * (x)
[/tex]
Rewriting:
[tex]V = (1/3) * (\pi) * (x ^ 2/4) * (x)
V = (1/12) * (\pi) * (x ^ 3)[/tex]
Answer:
An expression that represents the volume of the cone, in cubic units is:
[tex]V = (1/12) * (\pi) * (x ^ 3)[/tex]
