Calculate cone surface area in two steps. Find its base's area, which is the same as a circle's area, then find the cone's slanted area. Use this trick to build the right sized dunce hat or figure out a street cone's surface area. Use this concept, and clever subtraction, to figure out a volcano's surface area.
Find cone base area using a circle's formula, which is (π)(r)(r). Find cone slanted area with this formula: (1/2)(s)(C). Add the results to get the total surface area.
Measure the cone's circumference with this formula: C = πd. C is circumference and d is its diameter. Measure the diameter, which is a line from the base's one side, through its center, to the opposite side.
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Calculate cone slant height from its top to its base's side. Use your slant height and circumference measurement to calculate cone slanted area. Use step one's formula, where "s" is the slant height, and C is the circumference.
Add your results for cone base area and cone slanted area to get the total cone surface area.
If you have a cone with no base, like a "dunce hat," don't add the base area. There are different ways to figure cone surface area out. The different formulas used are based on one concept. You add cone slanted area to cone base area. The area of a circle is (π)(r)(r). Surface area is (1/2)(s)(C). Total area is (π)(r)(r) + (1/2)(s)(C).