How to Find the Surface Area of Any Cone

An ice cream cone shares a shape similar to its mathematical counterpart.

Students begin investigating the properties of cones in geometry class. These three-dimensional figures have a circular base at one end and a point called a vertex or apex at the other. You can visualize a cone by thinking of a spinning triangle. To find the surface area of a cone, you'll need to perform two steps: calculating the area of the base and then determining the surface area of the curved side.

Things You'll Need

• Ruler
• Calculator

Instructions

1. Measure the radius of the circular base of the cone.

2. Calculate the area of the base. The area of a circle is pi, approximated at 3.14, multiplied by the radius squared. For example, suppose your cone has a radius of 5 inches. You would calculate 5^2 x 3.14, or 25 x 3.14 = 78.5 square inches.

3. Find the area of the cone's side. First, measure the length of the cone's side. Make sure you use the same form of measurement as the radius. For example, suppose the cone measured 10 inches from the apex to a point on the circle that forms its base.

4. Multiply the side measurement by pi, approximated at 3.14. Then multiply that number by the radius. So in the example, you would calculate 10 x 3.14 x 5. This equals 157 square inches.

5. Add the amounts calculated in Steps 2 and 4 to determine the surface area of the cone. Concluding the example, 78.5 + 157 = 235.5 square inches.

Tips & Warnings

• Make sure you are consistent in your measurements.

References

• Math Is Fun: Cone Facts