Cylinder Calculator
Calculate volume, surface area, and lateral area of a cylinder. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Cylinder Calculator
Calculator
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Formula: Volume = πr²h | Surface Area = 2πr² + 2πrh
Worked example — Volume ≈ 62.83 m³, Surface Area ≈ 87.96 m²
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.
What is the difference between lateral surface area and total surface area?
Lateral surface area (2πrh) is only the curved 'label' portion of the cylinder — if you cut it and unrolled it flat, it would form a rectangle of width 2πr (the circumference) and height h. Total surface area adds the two flat circular caps (2 × πr²), giving the complete formula 2πr² + 2πrh, or equivalently 2πr(r + h).
What real-world objects and problems rely on cylinder volume calculations?
Cylindrical tanks (water, fuel, chemical storage), pipes and plumbing (flow capacity), soda cans and other packaging (material and content volume), and engine cylinders in combustion engines (displacement, which directly determines engine power) all depend on this same formula.
How does the cylinder volume formula relate to the cone and sphere formulas?
A cone with the same base radius and height as a cylinder holds exactly one-third its volume (V_cone = (1/3)πr²h), a relationship proven by Archimedes. A sphere inscribed in a cylinder of matching radius and height 2r has exactly two-thirds the cylinder's volume — Archimedes considered this cylinder/sphere volume relationship (2:3) one of his greatest discoveries and had it engraved on his tombstone.
Does the units used for radius and height matter for the volume result?
Yes — both radius and height must be in the same linear unit before applying the formula, and the resulting volume will be in that unit cubed (cm³, m³, in³, etc.). Mixing units (say, radius in centimeters and height in meters) without converting first is one of the most common sources of error in cylinder volume calculations.
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 for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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