Volume of a Cone Formula: How to Calculate & Examples

The volume of a cone formula is V = ⅓ × π × r² × t, where r is the base radius and t is the height. A cone's volume is exactly one third of a cylinder with the same base and height. The result is in cubic units (cm³, m³). π ≈ 3.14 or 22/7.

How to Calculate the Volume of a Cone + Example

Steps:

1. Find the base radius (r) and the height (t).
2. Square the radius (r²).
3. Multiply: V = ⅓ × π × r² × t.

Worked Example: A birthday hat shaped like a cone has a radius of 7 cm and a height of 12 cm. What is its volume? (π = 22/7)

Solution: V = ⅓ × (22/7) × 7² × 12 = ⅓ × (22/7) × 49 × 12 = ⅓ × 1,848 = 616 cm³

So the volume of the hat is 616 cm³.

Why It Matters for Students

The volume of a cone is part of the Curved Solids topic in Grade 9 and is frequently tested in school and national exams. It helps children find the capacity of real objects such as ice-cream cones, funnels, or piles of sand.

Fun fact: Three cones filled with water exactly fill one cylinder with the same base and height — which is why the ⅓ factor appears in the formula.

Also learn other solids: Volume of a Cylinder, Volume of a Sphere, Volume of a Cube, and Volume of a Cuboid. See also Surface Area of a Cylinder and all topics in the Mathematics hub.

Want your child to master maths with an experienced mentor? Try a free masterclass at Algonova.