Question

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

Answer 1

Answer:

$A. \frac{2}{3} \pi x^3$

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: $x$

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:

$V=\frac{\pi r^2h}{3}$

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:

$V=\frac{\pi x^2(2x)}{3}$

Rearranging the terms

$V=\frac{2\pi x^3}{3} \\V=\frac{2}{3} \pi x^3$

which is option A.