Surface Area of a Right Cone

Surface Area of a Right Cone

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

Cone

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

A cone is a 3D figure
that has
a [vertex], a [circle base],
and a [lateral face]
which is adjacent to the vertex and the base.

Right Cone

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

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

A = pi*r^2 + pi*r*h_s. A: Surface area of a right cone, r: Radius of the base, h_s: Slant height of the right cone

A = πr2 + πrhs

A: Surface area of a right cone
r: Radius of the base
hs: Slant height of the right cone
(= Distance between
the vertex and the rim of the base circle)

πr2: Base area
πrhs: Lateral area

Example

Find the surface area of the given right cone. r = 3, h = 4.

The radius of the base circle is 3.

So r = 3.

See this right triangle.

Starting from the shortest side,
the sides are (3, 4, hs).

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

Pythagorean triples

So hs = 5.

r = 3
hs = 5

So A = π⋅32 + π⋅3⋅5.

32 = 9
3⋅5 = 15

9 + 15 = 24

So A = 24π.