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Learn & check calculator

Understand what the answer means — cubic units, exact-π form, and why the radius is squared — then check it with the calculator.

Whether it is a homework problem or a diagram you are staring at, this page helps you reason through the learn & check calculator, then check your working with the live tool above.

How to work it out

  1. Measure across the circular end — the diameter or radius.
  2. If you measured the diameter, halve it to get the radius r.
  3. Square the radius and multiply by π to get the base area.
  4. Multiply the base area by the height h: V = π r² h.
  5. Convert the result into your preferred unit above.

Worked example. Take a cylinder with a diameter of 10 cm (so a radius of 5 cm) and a height of 25 cm. The base area is π × 5² = 78.54 cm², and multiplying by the height gives a volume of about 1.96 litres (1,963 cm³ · 0.52 US gallons).

For anything that holds liquid, measure the inside of the cylinder — the wall takes up space that the contents cannot.

Every learn & check page

Each page below targets a specific question and opens with the calculator ready to go:

Good to know

Is volume squared or cubed?
Volume is always cubic — it fills length, width and height. The radius is squared inside π r² only because that builds the flat circular base; the height supplies the third dimension.
What does 'volume in terms of π' mean?
It means leaving π in the answer instead of multiplying it out — for example 144π in³. It is the exact value, which the calculator can display via the 'Exact' precision setting.
How do I read the volume off a diagram?
Find the radius (or diameter) and the height on the figure, put them into V = π r² h in matching units, and compute. Enter the same numbers above to confirm your answer.

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