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Numbers · geometry · coneVolume of a cone — formula and calculator

Work out the volume of a cone with the formula V = ⅓ πr²h — 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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01

Calculator

enter the sizes — the formula and diagram follow

Cone

volume · surface
h = 4 cmr = 3 cml = 5 cm
diagram · not to scale
Result
Volume
37.6991cm³
= 0.0000376991 m³ = 0.0376991 L
Surface area
75.3982cm²
= 0.00753982 m²
How it was calculated
l = √(r² + h²) = √(3² + 4²) = 5 cm
V = ⅓ πr²h = 3.1416 × 3² × 4 / 3 = 37.6991 cm³
S = πr(r + l) = 3.1416 × 3 × (3 + 5) = 75.3982 cm²
← Other shapes and the composite shape
02

Formula

and what each letter means
Slant height
l = √(r² + h²)
Volume
V = ⅓ πr²h
Surface area
S = πr(r + l)
Notation
r
base radius
h
height — from the apex to the centre of the base
l
slant height — from the apex to the edge of the base
03

Worked example

with real numbers
Givenr = 3 cm, h = 4 cm
Solution
l = √(r² + h²) = √(3² + 4²) = 5 cm
V = ⅓ πr²h = 3.1416 × 3² × 4 / 3 = 37.6991 cm³
S = πr(r + l) = 3.1416 × 3 × (3 + 5) = 75.3982 cm²
Answer: volume — 37.7 cm³, surface area — 75.4 cm².
04

Common mistakes

A cone holds a third of a cylinder. Without the ⅓ the answer is three times too big.

Height and slant height are different segments: volume takes the height, surface takes the slant height.

05

Nearby shapes

Frustum of a coneV = ⅓ πh(R² + Rr + r²)CylinderV = πr²hPyramidV = ⅓ a²hCalculatorAll 19 shapes, the composite shape and hectares →
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