Geometry For Dummies, 3rd Edition
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To calculate the surface area of a cone, you need to add the area of the cone’s base to its lateral area. (The lateral area is a fancy name for the area of the surface that connects the base to the peak; in other words, everything but the base.)

geometry-cone
A cone with its height and slant height.

The following formula gives you the surface area of a cone.

geometry-cone-SA

Here’s a little more background on the lateral area:

The lateral area of a cone is one “triangle” that’s been rolled into a cone shape like a snow-cone cup (it’s only kind of a triangle because when flattened out, it’s actually a sector of a circle with a curved bottom side). Its area is

geometry-slant-height

Now for a cone problem:

geometry-cone-SAproblem

Here’s the proof diagram.

geometry-cone-proof

For the surface area, the only other thing you need is the slant height, l. The slant height is the hypotenuse of the 30-60-90 triangle, so it’s just twice the radius, which makes it

geometry-four-square-three

Now plug everything into the cone surface area formula:

geometry-SA-formula

About This Article

This article is from the book:

About the book author:

Mark Ryan is the founder and owner of The Math Center in the Chicago area, where he provides tutoring in all math subjects as well as test preparation. Mark is the author of Calculus For Dummies, Calculus Workbook For Dummies, and Geometry Workbook For Dummies.

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