18 min read

Volume of a Cone

A cone's volume is exactly one third of a cylinder with the same base and height.

One Third of a Cylinder

Solid explorer · cone

Radius 3Height 6

Volume ≈ 56.55 · Surface area ≈ 91.50

Change a value and watch:

A cone with the same radius and height as a cylinder always has exactly one third of its volume.

This \frac{1}{3} relationship is always true, for any radius and height.

Example 1 — volume of a cone

Find the volume of a cone with radius 3 and height 6 . Use π \approx 3.14 . 1 Base area: 3.14 \times 3^{2} = 28.26 2 Multiply by height: 28.26 \times 6 = 169.56 3 Take one third: 169.56 \div 3 Answer: 56.52

Example 2 — a larger cone

Find the volume of a cone with radius 5 and height 12 . Use π \approx 3.14 . 1 Base area: 3.14 \times 25 = 78.5 2 Multiply by height: 78.5 \times 12 = 942 3 Take one third: 942 \div 3 Answer: 314

Practice

Find the volume of a cone with radius 4 and height 9 . Use π \approx 3.14 .

Your answer