Cylinder Calculator
Calculate volume, surface area, and lateral area of a cylinder. Enter values for instant results with step-by-step formulas.
Reviewed by Manoj Kumar, Mathematics Educator
Formula
Volume = πr²h | Surface Area = 2πr² + 2πrh
A cylinder's volume equals its circular base area (πr²) multiplied by its height. Its total surface area adds the two circular caps (2πr²) to the curved lateral surface (2πrh), which unrolls into a rectangle of width equal to the circle's circumference.
Worked Examples
Example 1: Water storage tank
Problem:A cylindrical water tank has a radius of 2 meters and a height of 5 meters. Find its volume and total surface area.
Solution:Volume = π(2²)(5) = 20π ≈ 62.83 m³. Surface Area = 2π(2²) + 2π(2)(5) = 8π + 20π = 28π ≈ 87.96 m².
Result:Volume ≈ 62.83 m³, Surface Area ≈ 87.96 m²
Example 2: Soup can label size
Problem:A soup can has a radius of 3.5 cm and a height of 11 cm. What is the area of the label (lateral surface only)?
Solution:Lateral Surface Area = 2πrh = 2π(3.5)(11) = 77π ≈ 241.9 cm².
Result:Label area ≈ 241.9 cm²
Frequently Asked Questions
How is a cylinder's volume formula derived?
A cylinder's volume equals the area of its circular cross-section (πr²) multiplied by its height, V = πr²h — the same 'base area × height' logic used for any prism. This works because every horizontal slice through the cylinder is an identical circle of radius r, so stacking h units of that constant circular area straight up gives the total volume.
How is cylinder volume used to calculate liquid capacity in gallons or liters?
Compute the volume in cubic units first (πr²h), then apply a conversion factor: 1 cubic meter = 1,000 liters, and 1 US gallon ≈ 3,785.4 cubic centimeters. This two-step process — geometric volume, then unit conversion — is exactly how engineers size cylindrical fuel tanks and water storage cisterns to a target liquid capacity.
References
Reviewed by Manoj Kumar, Mathematics Educator · Editorial policy