Numbers · geometry · prismVolume of a prism — formula and calculator
Work out the volume of a prism with the formula V = S₀ × h — your numbers substituted and a diagram drawn. The surface area is calculated too. Units can be mixed, and the answer comes in the units you need, litres included.
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Calculator
enter the sizes — the formula and diagram follow02
Formula
and what each letter meansBase area
S₀ = n·a² / (4 tan(180° / n))
Volume
V = S₀ × h
Surface area
S = 2S₀ + n × a × h
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Worked example
with real numbersGivenn = 3, a = 4 cm, h = 10 cm
Solution
S₀ = n·a² / (4 tan(180° / n)) = 3 × 4² / (4 × tan(180° / 3)) = 6.9282 cm²
V = S₀ × h = 6.9282 × 10 = 69.282 cm³
S = 2S₀ + n × a × h = 2 × 6.9282 + 3 × 4 × 10 = 133.856 cm²
Answer: volume — 69.28 cm³, surface area — 133.9 cm².
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Common mistakes
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Nearby shapes
Rectangular boxV = a × b × cCylinderV = πr²hRegular polygonS = n·a² / (4 tan(180° / n))CalculatorAll 19 shapes, the composite shape and hectares →
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