Surface Area and Volume of a Cone

In geometry, a cone is a three-dimensional shape with a circular base and sides that converge to a single point. Is it a solid figure that you get when you rotate a triangle about its altitude.

You can compute the volume and surface area of a cone if you know its height and the radius of its base. The cone calculator below will tell you the surface area and volume if you input the height and radius, or you can apply the formulas described below.

Conical Volume Formula

For a cone with a radius of R and a height of H the formula for its volume is

Volume = (pi/3)R²H,

where pi is the constant 3.14159265358...

Example: Suppose a paper cone is 12 inches tall and the diameter of the base is 6 inches. So R = 3 and H = 12. Its volume is thus

(3.14159/3)(3²)(12) = 113.097 cubic inches.

Conical Surface Area Formula

For a cone with a radius of R and a height of H, the formula for its total surface area (including the base) is

Surface Area = (pi)(R)sqrt(R²+H²) + (pi)R².

For formula for surface area excluding the base of the cone is

Surface Area = (pi)(R)sqrt(R²+H²)

Example: Suppose a cone-shaped party hat is 14 inches tall and 9 inches wide. Since R = 4.5 and H = 14, the surface area (excluding the base) is

(3.14159)(4.5)sqrt(4.5²+14²) = 207.893 square inches.

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