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Volume of cylinders

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Volume of a Cylinder

The volume of a cylinder is V equals pi times radius squared times height. Square the radius, multiply by pi, then multiply by the height. A cylinder with radius 3 and height 7 has volume pi times 9 times 7, about 197.9 cubic units. Learn the steps and the radius-versus-diameter mistake to avoid.

The volume of a cylinder formula

The volume of a cylinder is V = πr²h, where r is the radius of the circular base and h is the height. This is the same "base area × height" idea used for any prism, since a cylinder's circular base has area πr².

Volume of a cylinder A cylinder with radius 3 and height 7. Its volume is pi times radius squared times height: pi times 9 times 7, approximately 197.9 cubic units. r = 3 h = 7 V = πr²h V = π × 3² × 7 V ≈ 197.9 units³
A cylinder with radius 3 and height 7 has volume π × 3² × 7, about 197.9 cubic units.
  1. Find the base area: multiply π by the radius squared (πr²).
  2. Multiply that base area by the height (h).
  3. Use 3.14 or the π key on a calculator for a decimal answer, or leave π in the answer for an exact value.

The formula uses the radius, not the diameter. If a problem gives the diameter, divide it by 2 first — using the diameter directly in the formula is one of the most common mistakes with this topic. Radius and diameter both come from circles and circumference.

A cylinder's volume formula is the circular version of the general prism rule — compare it to the volume of a prism. Volume measures the space inside the cylinder; it is different from the surface area of a cylinder, which measures its outside covering.

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