Surface Area of a Right Cone
How to find the surface area of a right cone: definition and its parts, formula, proof, example, and its solution.
This shape is called a cone.
A cone has a base (a circle) and a vertex.
The lateral face of a cone is the non-base face.
A right cone is a cone
whose height meets at the center of the base circle.
The slant height is the distance between
the vertex and the endpoint of the base circle.
A = πr2 + πrhs
A: surface area of a right cone
r: radius of the base
hs: slant height of the right cone
πr2: base area
πrhs: lateral area
Then, after cancelling 2π,
m∠[blue] / 360 = r / hs.
(base area) = πr2
(lateral area) = πhs2⋅(m∠[blue]/360)
Area of a circular sector
A = πr2 + πhs2⋅(m∠[blue]/360)
m∠[blue]/360 = r/hs
So A = πr2 + πhs2⋅(m∠[blue]/360)
= πr2 + πhs2⋅(r/hs)
= πr2 + πrhs.
See the right triangle in the cone.
Its legs are 3 and 4.
So it's a (3, 4, 5) triangle.
So hs = 5.
r = 3, hs = 5
A = π⋅32 + π⋅3⋅5