The complete surface ar area of a cone is the sum of the area of its base and the lateral (side) surface. The lateral surface ar area of a cone is the area the the lateral or side surface ar only.

since a cone is carefully related to a pyramid , the formulas for your surface locations are related.
Remember, the formulas for the lateral surface ar area of a pyramid is 1 2 ns together and also the total surface area is 1 2 p together + B . since the base of a cone is a circle, us substitute 2 π r because that p and π r 2 because that B wherein r is the radius that the basic of the cylinder. So, the formula because that the lateral surface area the a ideal cone is l . S . A = π r l , where together is the slant elevation of the cone .
instance 1:

discover the lateral surface area of a appropriate cone if the radius is 4 cm and also the slant elevation is 5 cm.

together . S . A = π ( 4 ) ( 5 ) = 20 π ≈ 62.82     centimeter 2

The formula for the complete surface area that a right cone is T . S . A = π r together + π r 2 .
example 2:

find the total surface area the a best cone if the radius is 6 inches and also the slant elevation is 10 inches.

T . S . A = π ( 6 ) ( 10 ) + π ( 6 ) 2 = 60 π + 36 π = 96 π   inch 2 ≈ 301.59   customs 2

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