Question

in the formula $v = pi r^{2}h$, the variable \$r$\ stands for
height
circumference
radius
diameter
the volume of a cylinder is $200pi$ $cm^{3}$ and its height is 8 cm. what is the radius of the base?
3 cm
10 cm
5 cm
4 cm

Explanation:

Step1: Recall cylinder volume formula

The volume formula of a cylinder is $V=\pi r^{2}h$, where $r$ represents the radius of the base - circle of the cylinder.

Step2: Solve for radius in second - part

Given $V = 200\pi\ cm^{3}$ and $h = 8\ cm$, substitute into $V=\pi r^{2}h$. We get $200\pi=\pi r^{2}\times8$. First, divide both sides of the equation by $\pi$: $200 = 8r^{2}$. Then divide both sides by 8: $r^{2}=\frac{200}{8}=25$. Take the square - root of both sides, $r = 5\ cm$ (we consider the positive value since radius is a non - negative quantity).

Answer:

In the formula $V=\pi r^{2}h$, the variable "r" stands for radius.
The radius of the base of the cylinder is 5 cm.