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Math Formulas > Geometry > Surface Area of a Cone

Surface Area of a Cone



r: the radius of the base
h: height
s: the slant height (the distance from any point on the base circle to the apex of the cone)

The surface area of a cone is given by:
SA = Π ∙ r2 + Π ∙ r ∙ s or SA = Π ∙ r ∙ (r + s)

Π defines the ratio of any circle's circumference to its diameter and is approximately equal to 3.141593, however the value 3.14 is often used.

Example: Determine the surface area of a cone that has the following properties:
r = 3 m
h = 6 m

step 1: the base area is: Abase = Π ∙ r2 = 3.14 ∙ 32 = 28.26 m2

step 2: determine s, the slant height s can be determined by using Pythagorean theorem.
s = √(r2 + h2 ) = √(32 + 62 ) = 3√5

step 3: the surface area of the cone is therefore:

SA = Abase + Π ∙ r ∙ s = 28.26 + 3.14 ∙ 3 ∙ 3√5 = 91.45 m2

Online Surface Area Calculator, click on the link will open a new window.
Mary
5/16/2010 11:38:22
Thank you so much! I have a math project due on soon and I wanted to find the surface area of a cone and I could not figure out what the "l" ment! My teacher said its the lateral face. I now know its the slant height! Thanks so much!
jl
5/28/2010 16:48:40
lol, this is the most viewed formula, crazy stuff
blah
6/20/2010 18:42:37
thnx 4 the help..got a math exam 2morrow..crazy stuff nd hrrible teacher!!!!

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