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 pl and the total surface area is 1 2 pl+B .

Since the base of a cone is a circle, we substitute 2πr 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=πrl , 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)=20π62.82 cm 2

The formula for the total surface area of a right cone is T.S.A=πrl+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 =60π+36π =96π inches 2 301.59 inches 2