Surface
Area of a
Cylinder
We need to calculate the surface
area of the top, base and body.
The top and base
of the cylinder are
both circles which
are equal.
The area of a
circle = πr2
Top and base can be
written as:
A = (πr2) x 2
If we were to “unwrap” the body of
the cylinder, it would be a
rectangle.
πd
h
•You already know that the area of a rectangle is L X W.
•In this case the width is the height of the cylinder.
•The length of the rectangle is actually the circumference of the cylinder.
•C = πd
So: A of the body = πdh
Put the two formula together and
the area of a cylinder is:
TOP
A = (πr2) x 2 + πdh
body
BASE
Let’s Try It!
Find the surface area of the
following cylinder.
First write out the formula of the area of a cylinder.
10 cm
A = (πr2)x2 + πdh
Identify the parts of the cylinder
that you need for the formula
15 cm
d = 20 cm
h = 15 cm
π = 3.14
r= 10 cm
Make the substitutions into
the formula and solve.
A = 2(πr2) +
πdh
= 2(3.14)(102) + (3.14)(20)(15)
A = 2(πr2) +
πdh
= 2(3.14)(102) + (3.14)(20)(15)
628
+
Circles
1570 cm2
942
Body
Find the Surface Area of the
Cylinder
5 cm
28 cm
A = 2(πr2) +
πdh
= 2(3.14)(52) + (3.14)(10)(28)
157
+
879.2
1036.2cm
Find the Surface Area of the
Cylinder (careful )
56 cm
22 cm
A = 2(πr2) +
πdh
= 2(3.14)(282) + (3.14)(56)(22)
4923.52 + 3868.48
8792 cm2