Right Cone: Surface Area

How to find the surface area of a right cone: definition, formula, 1 example, and its solution.

Cone

Definition

A cone is a 3D figure
that has a vertex, a circle base,
and a lateral face.

Right Cone

Definition

A right cone is a cone
whose vertex and the center of the base circle
are the endpoints of the height of the cone.

Formula

Formula

A = πr2 + πrhs

A: Surface area of a right cone
r: Radius of the base circle
hs: Slant height (= Height of the lateral face)

Example

Example

Solution

See this right triangle.

The radius of the base is 3.
The height is 4.
Set the slant height hs.

Then the sides of the triangle are (3, 4, hs).

So this right triangle is
a (3, 4, 5) right triangle.

Pythagorean Triple

So the slant height, hs, is 5.

r = 3
hs = 5

Then the surface area, A,
is equal to,
the base area, π⋅32

plus,
the lateral area, π⋅3⋅5.

So A = π⋅32 + π⋅3⋅5.

π⋅32 = 9π
+π⋅3⋅5 = +15π

9 + 15 = 24

So the surface area of the right cone is
24π.