Surface Area of a Right Cylinder
How to find the surface area of a right cylinder: definition, formula, proof, example, and its solution.
This shape is called a cylinder.
A right cylinder is a cylinder
whose centers of the bases
are the endpoints of the height.
A = 2⋅πr2 + 2πr⋅h
A: surface area of a right cylinder
r: radius of the base
h: height of the right cylinder
2⋅πr2: sum of the base areas
2πr⋅h: lateral area
Draw the net of a right cylinder.
There are two bases.
So the sum of the base areas is 2B = 2⋅πr2.
Area of a circle
See the lateral face in the net.
The lateral face is a rectangle.
Its width is the circumference (perimeter)
of the base circle:
P = 2πr.
And its height is h.
So the lateral area is Ph = 2πr⋅h.
Area of a rectangle
So A = 2B + Ph
= 2⋅πr2 + 2πr⋅h.
Surface area of a right prism
r = 4, h = 9
A = 2⋅π⋅42 + 2π⋅4⋅9