Surface Area of A Cone

Surface Area of Cone
The surface area of a cone is the total area of all its surfaces. A cone has two main surfaces:
A circular base: This is the flat bottom of the cone.
A curved lateral surface: This is the slanted side that connects the base to the apex (the pointed tip).
To calculate the total surface area, you add the area of the circular base and the area of the curved lateral surface.

The following diagram shows the formula for the surface area of cone. Scroll down the page for more examples and solutions for the surface area of cones.

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Formulas for the Surface Area of a Cone

1. Area of the Circular Base
   A_base = πr²
   where r = radius of the circular base
   
2. Area of the Curved Lateral Surface
   Curved Lateral Surface = πrl
   where l = slant height of the cone
   
3. Add both areas:
   SA = πr² + πrl
   

Finding the Slant Height (l)
Often, you are given the perpendicular height (h) of the cone (the distance from the apex straight down to the center of the base) and the radius (r). You’ll need to use the Pythagorean Theorem to find the slant height (l), as they form a right-angled triangle:

\(l^2 = r^2 + h^2\)
\(l = \sqrt{r^2 + h^2} \)

How to Find the Surface Area of a Cone?

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How to Find the Surface Area of a Cone When Not Given the Slant?

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Example of how to find the surface area of a cone

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Find the Lateral Area, Surface Area and Volume of a cone given the height and radius in simplest π form

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