1. Surface Area of a Cylinder

2. 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

3. If we were to “unwrap” the body of the cylinder, it would be a rectangle.
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

4. Put the two formula together and the area of a cylinder is:
TOP
A = (πr2) x 2 + πdh
body
BASE

5. 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
A = 2(πr2) πdh
= 2(3.14)(102) + (3.14)(20)(15)
Make the substitutions into the formula and solve.

6. A = 2(πr2) + πdh = 2(3.14)(102) + (3.14)(20)(15)
Circles Body
1570 cm2

7. Find the Surface Area of the Cylinder
5 cm
28 cm

8. A = 2(πr2) + πdh = 2(3.14)(52) + (3.14)(10)(28)
1036.2cm

9. Find the Surface Area of the Cylinder (careful )
56 cm
22 cm

10. A = 2(πr2) + πdh = 2(3.14)(282) + (3.14)(56)(22)
8792 cm2