Volume of a Sphere Formula
Geometry Formulas: Area, Volume, Perimeter
What is the formula for the volume of a sphere?
Answer
Volume of a sphere
V = (4/3) · π · r³
Here r is the radius. The result comes out in cubic units.
Where the formula comes from
V = (4/3) · π · r³
Archimedes proved it and asked for it on his tombstone: a sphere fills exactly two thirds of the smallest cylinder that contains it. That cylinder has radius r and height 2r, so its volume is 2πr³, and two thirds of that is (4/3)πr³.
Worked examples
Let r = 3. Then the volume of a sphere ≈ 113.1 cubic units.
Let r = 5.5. Then the volume of a sphere ≈ 696.91 cubic units.
The common mistake
Cubing the diameter. The radius is cubed here, so a diameter in its place makes the answer eight times too big — the worst of the three radius traps, because the error grows with the power.
Other quantities: Sphere
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- Gravel Calculator - Area to cubic yards, tons and coverage
- Topsoil Calculator - Cubic yards, weight and coverage for any area
- Multiplication Facts - Any two numbers from 1 to 9, with the working shown
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Values from the Formula
| If r = | Volume |
|---|---|
| 1 | ≈ 4.19 cubic units |
| 2 | ≈ 33.51 cubic units |
| 3 | ≈ 113.1 cubic units |
| 4 | ≈ 268.08 cubic units |
| 5 | ≈ 523.6 cubic units |
| 10 | ≈ 4,188.79 cubic units |
Geometry Formulas: Area, Volume, Perimeter
These are the formulas for the area, perimeter, circumference, volume and surface area of the standard shapes — 31 of them. Each page shows not only the formula but where it comes from, what every letter stands for, two worked examples and the mistake that this particular shape invites. For example, it can help you find out what is the formula for the volume of a sphere? (The answer is: V = (4/3) · π · r³). Pick the pair — "Area of a circle", for instance — and hit the "Find out" button.
Geometry Formulas: Area, Volume, Perimeter