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Volume of a Sphere

A sphere's volume uses the radius cubed, scaled by a fixed factor of $\dfrac{4}{3}$.

Radius Cubed

Solid explorer · sphere

Radius 3

Volume ≈ 113.10 · Surface area ≈ 113.10

Change a value and watch:

Increase the radius and watch the volume grow very quickly — it depends on the CUBE of the radius.

Doubling a sphere's radius multiplies its volume by 8 (since 2^{3} = 8).

Example 1 — volume of a sphere

Find the volume of a sphere with radius 3 . Use π \approx 3.14 . 1 Cube the radius: 3^{3} = 27 2 Multiply by π: 3.14 \times 27 = 84.78 3 Multiply by \frac{4}{3} : 84.78 \times 4 \div 3 = 339.12 \div 3 Answer: 113.04

Example 2 — a larger sphere

Find the volume of a sphere with radius 6 . Use π \approx 3.14 . 1 Cube the radius: 6^{3} = 216 2 Multiply by π: 3.14 \times 216 = 678.24 3 Multiply by \frac{4}{3} : 678.24 \times 4 \div 3 = 2712.96 \div 3 Answer: 904.32

Practice

Find the volume of a sphere with radius 5, to 2 decimal places. Use π \approx 3.14 .

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