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:

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.

### 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 + √(h^{2} + r^{2})]

SA = π(4)[4+ √(6^{2} + 4^{2})] = 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 + √(h^{2} + r^{2})]

SA = π(1)[1+ √(1^{2} + 1^{2})] = π(1)[2.414] = 7.584

3.) **The surface area of the cone is 7.584.**