Volume of Cone Calculator
Volume
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Slant Height
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Lateral Surface Area
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Total Surface Area
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How to Calculate the Volume of a Cone
The volume of a cone is exactly one-third the volume of a cylinder with the same base and height: V = (1/3)πr²h. This elegant relationship means a cone holds one-third the liquid of a cylinder with matching dimensions.
The slant height is the distance from the tip to any point on the base edge: l = √(r² + h²). The lateral surface area (curved surface) is LSA = πrl, and the total surface area including the circular base is TSA = πr(r + l).
Cones appear in ice cream cones, traffic pylons, funnels, and architectural structures. Volume calculations help determine capacity, while surface area is useful for material estimation in manufacturing and construction projects.
Frequently Asked Questions
What is the volume of a cone?
V = (1/3)πr²h. A cone with radius 3 and height 12 has volume = (1/3) × π × 9 × 12 ≈ 113.1 cubic units.
How is a cone's volume related to a cylinder?
A cone's volume is exactly one-third of a cylinder with the same radius and height. Three cones fill one cylinder.
What is slant height?
Slant height is the distance from the tip of the cone to the edge of the base, measured along the surface: l = √(r² + h²).
How do you find the surface area of a cone?
Total surface area = πr(r + l), where l is the slant height. This includes the circular base (πr²) plus the lateral surface (πrl).