Answer:
[tex]A. \frac{2}{3} \pi x^3[/tex]
Step-by-step 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: [tex]x[/tex]
and we are told that the height is twice the radius, so:
height: [tex]2x[/tex]
and now we use the formula to calculate the volume of a cone:
[tex]V=\frac{\pi r^2h}{3}[/tex]
where [tex]V[/tex] is volume, [tex]r[/tex] is radius, and [tex]h[/tex] is the height. and [tex]\pi[/tex] is a constant
in this case
[tex]r=x[/tex]
[tex]h=2x[/tex]
so we substitute thisvalues in the formula for the volume:
[tex]V=\frac{\pi x^2(2x)}{3}[/tex]
Rearranging the terms
[tex]V=\frac{2\pi x^3}{3} \\V=\frac{2}{3} \pi x^3[/tex]
which is option A.
