Volume of a Cylinder Math Example 2

Follow the full solution, then compare it with the other examples linked below.

medium

A cylindrical water tank holds

2000\pi

liters. Its height is 20 m. Find the radius of the tank.

1
Step 1: Use the formula $V = \pi r^2 h$ and substitute $V = 2000\pi$ and $h = 20$ .
2
Step 2: $2000\pi = \pi r^2 \times 20$ .
3
Step 3: Divide both sides by $20\pi$ : $r^2 = \frac{2000\pi}{20\pi} = 100$ .
4
Step 4: Take the square root: $r = \sqrt{100} = 10$ m.

Answer

The radius is

10

To find the radius from the volume and height, rearrange the cylinder formula:

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

, then take the square root. Note that

\pi

cancels nicely here because the volume was given as a multiple of

\pi

About Volume of a Cylinder

The amount of three-dimensional space inside a cylinder, found by multiplying the area of the circular base by the height.

A cylinder has a radius of 4 cm and a height of 10 cm. Find its volume. Use [formula].

A soup can has a diameter of 8 cm and a height of 12 cm. Find the volume. Leave your answer in terms

Two cylinders have the same volume. Cylinder A has radius 3 and height 16. Cylinder B has height 4.