Numbers · geometry · frustum of a coneVolume of a frustum — formula and calculator
Work out the volume of a frustum with the formula V = ⅓ πh(R² + Rr + r²) — 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 meansSlant height
l = √((R − r)² + h²)
Volume
V = ⅓ πh(R² + Rr + r²)
Surface area
S = π(R² + r² + (R + r)l)
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Worked example
with real numbersGivenR = 5 cm, r = 3 cm, h = 4 cm
Solution
l = √((R − r)² + h²) = √((5 − 3)² + 4²) = 4.47214 cm
V = ⅓ πh(R² + Rr + r²) = 3.1416 × 4 × (5² + 5 × 3 + 3²) / 3 = 205.251 cm³
S = π(R² + r² + (R + r)l) = 3.1416 × (5² + 3² + (5 + 3) × 4.47214) = 219.211 cm²
Answer: volume — 205.3 cm³, surface area — 219.2 cm².
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Common mistakes
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Nearby shapes
ConeV = ⅓ πr²hCylinderV = πr²hPyramidV = ⅓ a²hCalculatorAll 19 shapes, the composite shape and hectares →
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