The volume of a cone is the amount of three-dimensional space enclosed by the cone. A cone has a circular base and a pointed top called the vertex. The radius is the distance from the center of the base to its edge, and the height is the perpendicular distance from the base to the vertex.
Volume of a Cone Formula
To calculate the volume of a cone, you multiply the area of the base by the height and then take one-third of that product. The formula is:
Volume = (1/3) × π × r² × h
where r is the radius of the base, h is the height, and π (pi) is a mathematical constant approximately equal to 3.1416 that represents the ratio of a circle’s circumference to its diameter.
Cones are often classified as either right circular cones, where the vertex is directly above the center of the base, or oblique cones, where the vertex is off-center. The volume formula applies to both, as long as the height is measured perpendicularly from the base to the vertex.
How to Find the Volume of a Cone Example
Find the volume of a cone with a radius of 4 cm and a height of 9 cm.
Step 1: Square the radius
4 × 4 = 16
Step 2: Multiply by the height
16 × 9 = 144
Step 3: Multiply by π
144 × 3.1416 ≈ 452.39
Step 4: Take one-third
452.39 ÷ 3 ≈ 150.80
Answer: The volume of the cone is approximately 150.80 cm³.
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