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Surface Area of a Cone

The total surface area of a cone is the sum of the area of its base and the lateral (side) surface.

The lateral surface area of a cone is the area of the lateral or side surface only.

Since a cone is closely related to a pyramid , the formulas for their surface areas are related.

Remember, the formulas for the lateral surface area of a pyramid is 1 2 p l and the total surface area is 1 2 p l + B .

Since the base of a cone is a circle, we substitute 2 π r for p and π r 2 for B where r is the radius of the base of the cylinder.

So, the formula for the lateral surface area of a right cone is L . S . A = π r l , where l is the slant height of the cone .  

Example 1:

Find the lateral surface area of a right cone if the radius is 4 cm and the slant height is 5 cm.

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

The formula for the total surface area of a right cone is T . S . A = π r l + π r 2 .

Example 2:

Find the total surface area of a right cone if the radius is 6 inches and 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 inches 2