How to Find the Area of a Cone Shape

Cones are used as traffic markers.

Cone shapes are composed of a circular base and a pyramidal top. Cones are often used for markers such as traffic cones or cones on a practice field to tell players where to go. The surface area of a cone represents the space covered by the outside of the cone. You may want to know the surface area if you are determining how much paint you need to paint a cone. You can find this by adding the area of the bottom circle and the area of the lateral (cone) surface.

Things You'll Need

• Calculator
• Ruler

Instructions

1. Measure the diameter of the base of the cone and the slant length. The diameter is the distance across the circle on the bottom of the circle through the center. The slant length is the distance from the bottom of the cone, up the side of the cone, to the top.

2. Divide the diameter by two to calculate the radius.

3. Multiply the radius times the radius times pi (approximately 3.14) to calculate the surface area of the bottom of the cone. For example, if the radius is 5 inches, you would multiply 5 x 5 x 3.14 to get 78.5 square inches.

4. Multiply the radius times the slant height times pi to calculate the surface area of the remainder of the cone. In this example, if the slant height is 6 inches, you would multiply 5 x 6 x 3.14 to get 94.2 square inches.

5. Add the results from steps 3 and 4 to find the total surface area of the cone shape. In this example, you would add 94.2 and 78.5 to get 172.7 square inches.

References

• Math Guide: Surface Area Lessons