Volume is the amount of space a 3-dimensional figure occupies. Since a cylinder has a round base one way to think of volume is to think of putting one circle on top of another circle to “fill” the cylinder as shown in the figure below.

Determining the Volume of a Cylinder

1. Find the area of the base. It is a challenge to count the number of cubes in the first layer of a cylinder, since the first layer of a cylinder will have many partial cubes. Put the pieces together to form whole units.

   

   Find the area of the circle using formula for a circle: A = πr².

2. Multiply the area of the circle by the height, the number of circles layered on top of each other to fill the cylinder.

Answer the following questions. Click the blanks to reveal the answers.

• The base has a radius of Interactive popup. Assistance may be required. __________ 3 units .
• The formula used to find the area of a circle is Interactive popup. Assistance may be required. __________ A = πr² .
• The area of the base of the cylinder is Interactive popup. Assistance may be required. __________ A = π(3)² = 9π units² .
• The height of the cylinder is Interactive popup. Assistance may be required. __________ 8 units .
• Volume is found by Interactive popup. Assistance may be required. __________ multiplying the area of the Interactive popup. Assistance may be required. __________ base by the Interactive popup. Assistance may be required. __________ height .
• The volume of the cylinder is Interactive popup. Assistance may be required. __________ V = 9π ⋅ 8 = 72π ≈ 226.08 cubic units .

The formula for the volume of a cylinder is V = πr² ⋅ h.

V = πr² ⋅ h OR V = B ⋅ h

* The letter “B” is the area of the base of the cylinder (the area of the circle), and “h” represents the height of the cylinder.

Watch this video summarizing the formula of the volume of a cylinder.

1. Follow this link to Volume of a Cylinder Interactive. The link will open in a new browser window or tab.
2. Scroll down to the blue box titled, Find the Volume of a Cylinder.
3. Click Next to work through a practice problem. Use your calculator to help you with computation. Follow the on-screen prompts to proceed through the steps of the problem.
4. At the end of the problem, you will see a summary screen. You may wish to copy that information into your notes for your future reference.

Example: Perry Poppins sells flavored popcorn in cylindrical containers. One container has a diameter of 6 inches and a height of 8 inches. A second container has a diameter of 8 inches and a height of 6 inches.

Raquel Poppins says that the two containers should be priced the same because the containers hold the same amount. Tamika Poppins says that the containers do not hold the same amount and should not be priced the same.

Who is correct and why?

Answer the following questions. Click the blanks to reveal the answers.

• The formula for the volume of a cylinder is Interactive popup. Assistance may be required. __________ V = πr² ⋅ h or V = B ⋅ h .
• The radius of Cylinder 1 is Interactive popup. Assistance may be required. __________ 4 inches .
• The height of Cylinder 1 is Interactive popup. Assistance may be required. __________ 6 inches .
• The volume of Cylinder 1 is Interactive popup. Assistance may be required. __________ V = π(4 in.)² ⋅ 6in. = 16 in.² π(6in.) = 96π in.³ = 301.6 in.³ .
• The radius of Cylinder 2 is Interactive popup. Assistance may be required. __________ 3 inches .
• The height of Cylinder 2 is Interactive popup. Assistance may be required. __________ 8 inches .
• The volume of Cylinder 2 is Interactive popup. Assistance may be required. __________ V = π(3 in.)² ⋅ 8in. = 9 in.² π(8in.) = 72π in.³ = 226.2 in.³ .
• The volume of Cylinder 1 is Interactive popup. Assistance may be required. __________ 301.6 in.³ . The volume of Cylinder 2 is Interactive popup. Assistance may be required. __________ 226.2 in.³ .
• Would they both contain the same amount of popcorn and cost the same? Interactive popup. Assistance may be required. __________ No .
• Which container would contain the most popcorn and cost more? Interactive popup. Assistance may be required. __________ Cylinder 1