Volume of a Cylinder: Formula, Examples and Practice

Why it’s the circle times the height

Picture a stack of coins. Every coin is the same circle.

The space the stack takes up is the area of one coin times how tall the stack is. Add coins and the stack gets taller, but each circle stays the same size.

That’s all V = πr²h says. The area of a circle is πr². Multiply it by the height, h, and you have the volume.

The catch? The formula wants the radius, r. That’s the distance from the center of the circle to its edge.

The diameter goes all the way across, so it’s twice as long. If a question gives you the diameter, halve it first.

This page uses 3.14 for π, like our practice questions. The π key on the GED calculator uses more decimal places, so your last digit can come out a little different. Round the way the question asks.

Bottom line: get the radius, square it, then multiply by 3.14 and the height.

Example 1: a can of soup

Notice the word across. When a question tells you how far it is across a circle, that’s the diameter.

Example 2: a kiddie pool in gallons

Volume comes out in cubic inches or cubic feet. A pool or a tank is usually measured in gallons, so you switch at the end.

One gallon is exactly 231 cubic inches. One cubic foot holds about 7.48 gallons. So divide cubic inches by 231, or multiply cubic feet by 7.48.

Measured in feet, the same pool is 5 feet across and 1 foot deep. That’s 19.625 cubic feet, and 19.625 × 7.48 is about 147 gallons again.

Example 3: work backward to the height

Some questions give you the volume and ask how tall the cylinder is. Find the area of the circle first, then divide.

4 mistakes that cost points

Mistake 1: using the diameter as the radius

Square the 3 inches from the soup can and you get 113.04 cubic inches. That’s four times the real answer. Halve any distance across before you square it.

Mistake 2: forgetting to square the radius

r² means r × r. Skip the square in the water tank example and you divide 628 by 15.7. That gives a tank 40 feet tall, five times the real height.

Mistake 3: mixing inches and feet

Put every length in the same unit before you multiply. A tank 4 feet across and 30 inches tall? Use 2.5 feet for the height: 3.14 × 2² × 2.5 = 31.4 cubic feet.

Mistake 4: writing square units

The circle in the water tank covers 78.5 square feet. Multiply by the 8-foot height, and you get 628 cubic feet. Volume is always in cubic units.

Practice: 5 new questions

Every set is new. Check each answer as you go, and read the working on any you miss before the next one.

Want more? Practice all of geometry and measurement (25 questions, every skill in the topic), or take the full GED math practice test.