Geometry

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Surface Area of a Cone

Cone Surface Area Formula

The formula for surface area of a cone is given as:
cone surface area formula
Where SA is the surface area, h is the height of the cone, and r is the radius of the circle at the cone’s base.

surface area of a cone

Example Problems

Problem 1:
Find the surface area of a cone with a height of 6 and a radius of 4.
Solution:
1.) We have both required dimensions to use the surface area formula.
2.) Plugging the height and radius in, we get:
SA = πr[r + √(h2 + r2)]
SA = π(4)[4+ √(62 + 42)] = π(4)[11.2111] = 140.883
3.) The surface area of the cone is 140.883.

Problem 2:
Find the surface area of a cone with a height of 1 and a radius of 1.
Solution:
1.) We have both required dimensions to use the surface area formula.
2.) Plugging the height and radius in, we get:
SA = πr[r + √(h2 + r2)]
SA = π(1)[1+ √(12 + 12)] = π(1)[2.414] = 7.584
3.) The surface area of the cone is 7.584.

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