Learn · Algebra and geometry (grades 8–10)

How to Find the Volume of a Cylinder

The volume of a cylinder is how much it holds, in cubic units. A cylinder is a stack of circles, so its volume is the area of the circular base times the height.

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The steps

  1. Find the radius of the circular base (half of the diameter) and the height.
  2. Find the area of the base: π × r².
  3. Multiply the base area by the height: V = π × r² × h.
  4. Leave the answer in terms of π, or multiply by 3.14159 for a decimal.
  5. Write the units as cubic units, such as cm³ or in³.

A worked example

Find the volume of a cylinder with radius 3 cm and height 10 cm.

  1. Base area: π × 3² = 9π.
  2. Multiply by the height: 9π × 10 = 90π.
  3. As a decimal: 90 × 3.14159 ≈ 282.74.

The volume is 90π cm³, which is about 282.74 cm³.

Why it works

Slice the cylinder into very thin coins. Each coin has the area of the circular base, πr², and a tiny thickness. Stack them up to the height h and you get πr² times h. This is the idea behind every prism: base area times height. A can of soup, a pipe and a tower of coins are all cylinders, and the same rule gives the volume of each.

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Common mistakes

Questions people ask

How is a cylinder's volume like a box's?

Both are base area times height. A box's base is a rectangle, and a cylinder's base is a circle.

How do I convert cubic centimeters to liters?

1,000 cm³ = 1 liter, so 282.74 cm³ is about 0.28 liters.

What is the surface area?

2πr² (two circles) plus 2πrh (the side wrapped around).

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