Cone Surface Area Formula

The formula for surface area of a cone is given as:

$$SA=\pi r(r+\sqrt{h^{2}+r^{2}})$$

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

Let's go through a couple of example problems together to practice finding the surface area of a cone.

Example 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.

Example 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.