Question

1. what is the height of a cylinder with a volume of 500π cm³ and a radius of 5 cm?

a. 12 cm
b. 10 cm
c. 15 cm
d. 20 cm

Explanation:

Step1: Recall volume formula

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

Step2: Substitute given values

We know $V = 500\pi$ and $r = 5$. Substituting into the formula gives $500\pi=\pi\times5^{2}\times h$.

Step3: Simplify the equation

First, calculate $5^{2}=25$. The equation becomes $500\pi=\pi\times25\times h$. Divide both sides of the equation by $25\pi$. So, $h=\frac{500\pi}{25\pi}$.

Step4: Solve for h

The $\pi$ terms cancel out, and $\frac{500}{25}=20$. So $h = 20$ cm.

Answer:

d. 20 cm