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

due to the fact that a cone is closely related come a pyramid , the recipe for your surface areas are related.
Remember, the formulas because that the lateral surface ar area the a pyramid is 1 2 ns together and also the complete surface area is 1 2 p together + B . due to the fact that the base of a cone is a circle, us substitute 2 π r for ns and also π r 2 because that B wherein r is the radius the the basic of the cylinder. So, the formula for the lateral surface area the a right cone is together . S . A = π r together , whereby l is the slant elevation of the cone .
instance 1:

uncover the lateral surface area that a appropriate cone if the radius is 4 cm and the slant elevation is 5 cm.

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

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

find the full surface area that a right cone if the radius is 6 inches and also the slant height is 10 inches.

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

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