# How to Find the Radius of a Cylinder When Given the Volume and Height

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A cylinder is a three-dimensional object that looks like a rod with circular ends. If you know the volume of a cylinder and its height, you can determine its radius using the same formula used to calculate its volume when you do know the radius. Keep in mind that the radius is one half of the cylinder's diameter, or the distance from the center of either end to its edge.

## 1. Know the Formula for the Volume of a Cylinder

The formula for the volume of a cylinder contains three elements: the radius of the cylinder (r), the height (h) of the cylinder, and the ratio of the circumference of a circle to its diameter pi. To find the volume of a cylinder, you multiply pi by the cylinder's height and the square of its radius. Pi is approximately 3.14159 and can be rounded down to 3.14 if your calculator doesn't have a pi key. Here is the formula in mathematical terms:

V = pi x h x r^2

## 2. Solve for the Radius (r)

Since you want to find the radius of the cylinder, you need to rearrange the formula to solve for the term r, which is the radius. First, divide both sides by pi and h. These terms will cancel on the right side of the equation, leaving only r^2. Now take the square root of both sides to get rid of the square on the radius. This leaves us with the following:

r = square root of (V / (pi x h))

Now just plug your numbers into the equation and compute the radius. For example, if your cylinder has a height of 10 centimeters and a volume of 30 cubic centimeters, the calculation would look like the following:

r = square root of (30 cm^3 / (3.14 x 10 cm)) = 0.98 cm