Surface area of a cone

P=\pi r^2+\pi r l

Result unit: area units

What it describes

The surface area of a cone (the base and the lateral surface);

l

is the slant height.

P

surface area

r

base radius

l

slant height

The area is the base (a circle) plus the lateral surface (a sector of a circle);

l

is the slant height — the distance from the apex to the edge of the base.

Surface area of a cone; the slant height is found from

l=\sqrt{r^2+H^2}

Radius 3, slant height 5. Find the total surface area of the cone.

Substitution

r=3

l=5

Result

P=\pi\cdot9+\pi\cdot3\cdot5=24\pi\approx75.4

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