# How to Calculate the Volume of a Cylinder

The volume of a cylinder formula is an equation used to calculate the amount of space taken up by a cylinder. A cylinder is a 3-D shape with circles as its end faces. A can, pillar candle, and glue stick are examples of cylinders. This article will discuss the components of this formula and 5 common examples.

### Where does the formula come from?

The volume of a cylinder formula is v= πr²h. The value π is a constant that relates to all circles. It is the ratio of a circle’s circumference to its diameter. The radius of the cylinder’s face is defined as r. This value is half of the face’s length, or diameter. The height of the entire shape is defined as h.

A key component of this formula is for formula for the area of a circle, A=πr². In the area of a circle equation, π and rrelate to the same dimensions as before. The volume of a cylinder formula first takes the area of the cylinder’s face. This face is a circle. Then it multiplies it by the height of the cylinder. This extends it to a three-dimensional or cubic value. That is how the volume of a cylinder calculator is derived.

### Example 1

Let’s apply this formula to an example. The can above has a radius of 2.5 inches and a height of 5 inches. The first step is to rewrite our equation and replace r and h with the known values.

v= πr²h

v= π * (2.5 in)² * 5 in

Always remember your units! Our solution should have a unit of in³. If it does not, there was an error along the way.

The second step is to begin operations. These should be done following usual order of operations, or PEMDAS. Start by squaring the radius. This should leave a value in square inches, in².

v= π * 6.25 in² * 5 in

v= π * 31.25 in²

Depending on your goals, leaving the answer in the form of 31.25π in³ can suffice. This is always the most accurate form. Pi is an irrational number. Therefore, multiplying 31.25 times π will always require a rounded product.

If necessary, we will multiply pi times 31.25. This product will be rounded to two decimal places, or the hundredths place.

v= 98.17 in³

That is how you apply the volume of a cylinder formula!

### Example 2

Let’s use the volume of a cylinder calculator to find the volume of a cylinder with r = 9.1 cm and h = 3.6 cm.

The final solution is 936.56 cubic centimeters. This volume was also rounded to two decimal places.

v= πrh²

v= π * (9.1 cm)² * 3.6 cm

v= π * 82.81 cm² * 3.6 cm

v= π * 298.116 cm³

v= 936.56 cm³

The final solution is 936.56 cubic centimeters. This volume was also rounded to two decimal places.

### Example 3

Find the volume of a cylinder with a diameter of 20 ft and height of 97 ft.

First, we’ll have to find the radius. The diameter is two times the radius. This means we must divide the diameter by 2.

r= d/2

r= 20 ft/2

r= 10 ft

The radius is 10 feet. Now the volume of a cylinder formula can be applied.

v= πrh²

v= π * (10 ft)² * 97 ft

v= π * 100 ft² * 97 ft

v= π * 9700 ft³

v= 30,473.449 ft³

The cylinder has a volume of 30,473.449 cubic feet. Unlike the previous examples, this one was rounded to three decimal places.

### Example 4

Find the volume of a cylinder with r = 14 m and h = 14 m.

The volume is 8,620.53 cubic meters.

v= πrh²

v= π * (14 m)² * 14 m

v= π * 196 m² * 14 m

v= π * 2744 m³

v= 8,620.53 m³

The volume is 8,620.53 cubic meters.

### Example 5

Fine the volume of a cylinder with r = 7.125 in and h = 8.25 in.

v= πrh²

v= π * (7.125 in)² * 8.25 in

v= π * 50.765625 in² * 8.25 in

v= π * 418.8164063 in³

v= 1,315.75 m³

The volume is 1,315.75 cubic inches. It is recommended to hold off on rounding until final step. Carry out all intermediate operations to as many decimal places as possible. This will produce the most accurate answer.

The volume of a cylinder formula gives anyone the ability to find the volume of a cylinder without having to reach for complex 3-D geometry. In a few simple steps, a volume is found in cubic units. Time to show how you’ve become a pro at using the volume of a cylinder calculator!

Author: Khaiylah Bustamante

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