Understand the right circular cylinder

A right circular cylinder has two congruent parallel circular bases whose centres are joined by an axis perpendicular to both base planes. The calculators model the closed solid, including both bases in total surface area.

Properties that make the calculations work

Unrolling the lateral surface gives a rectangle with height h and width 2πr. This explains the lateral area 2πrh. Volume is the base area πr² multiplied by the perpendicular height.

Where the model is useful

Use the inverse tools for a target capacity or known total area. An open-top container needs a different area expression, and its material thickness reduces internal capacity.

Measure the right thing

Total surface area here includes two bases. Slanted cylinders and open containers need different surface models.

Sketch the figure and mark every known measurement before choosing a calculator. A length measured along an edge is not automatically a perpendicular height. If a formula needs a radius, check that the value has not been measured across a full diameter. Write the unit beside each known quantity before entering it.

Scale and units

Multiplying every length by k multiplies any area by k² and any volume by k³. This is a useful check: doubling all dimensions cannot merely double an area. Inputs expressed in centimetres produce cm² for area and cm³ for volume; the unit selector relabels rather than converts entered numbers.

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Wolfram MathWorld: Right circular cylinder provides reference reading. Our summaries and examples are written for this portal and are not a specialist-reviewed textbook. Try a worked example or suggest a correction.