Question

The volume of a cylinder is 4 pi x3 cubic units and its height is x units.
Which expression represents the radius of the cylinder, in units?
2x
4x 2 pi x2 4 pi x2

Answer 1

Answer:

$2x$

Step-by-step explanation:

The volume of a cylinder, $V$ is given by the formula,

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

Where, $r$ is the radius and $h$ is the height of the cylinder.

Here, $V=4\pi x^{3}$, $h=x$. Plug in these values and solve for radius, $r$.

This gives,

$V=\pi r^{2}h\\4\pi x^{3}=\pi r^{2}x\\r^{2}=\frac{4\pi x^{3}}{\pi x}\\r^{2}=4x^{2}$

Taking square root both sides, we get

$\sqrt{r^{2}}=\sqrt{4x^{2}}\\r=2x$

Therefore, the radius of the cylinder can be expressed as $2x$.