Question

in the formula v = πr²h, the variable
\ stands for ______. a. height b. circumference c. radius d. diameter the volume of a cylinder is 200π cm³ and its height is 8 cm. what is the radius of the base? a. 3 cm b. 10 cm c. 5 cm d. 4 cm

Explanation:

Step1: Recall cylinder - volume formula

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

Step2: Answer the first question

In the formula $V = \pi r^{2}h$, the variable "r" stands for the radius of the base of the cylinder. So the answer to the first question is c. radius.

Step3: Solve for the radius in the second - question

Given $V = 200\pi\ cm^{3}$ and $h = 8\ cm$. Substitute these values into the volume formula $V=\pi r^{2}h$:
$200\pi=\pi r^{2}\times8$.
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 take the positive value since radius is a non - negative quantity).

Answer:

1. c. radius
2. c. 5 cm