Finding the Surface Area of a Cylinder: Lesson
 Topic Index | Grade 7 Math | Intermediate Test Prep | StudyZone
 

The surface area of a 3-dimensional, or solid figure is equal to the sum of all of it's faces.
In the case of a cylinder, to find it's surface area you need to find the area of it's two congruent circular bases, and it's tube, or curved side. 
The curved side flattens into a rectangle.

 

 

 

 

 

 

 


Surface Area of a Cylinder
Formula:

SA = 2(Π)(r2) + (Π)(d)(h)
(the 2 circular bases) + (rectangular region)

In the diagram above:
d = 4"
r = 2"
h = 6"
let pi = 3.14
Plug in the values:
SA = 2(3.14)(22) + (3.14)(4)(6)
SA = 25.12 + 75.36
SA = 100.48 square inches!

 

Let's start with an easy example.


A can has a diameter of 8" and is 10" tall.  What is it's surface area?

SA = 2Π r2 + Π dh
In this problem:
d = 8"
r = 4"
h = 10"
let pi = 3.14
SA = 2(3.14)(42) + (3.14)(8)(10)
SA = 100.48 + 251.20
SA = 351.68 square inches!
 

  Let's try another...

             

What is the surface area of this shape?

 

SA = 2Π r2 + Π dh
d = 15'
r = 7.5'
h = 24'
let pi = 3.14
SA = 2(3.14)(7.52) + (3.14)(15)(24)
SA = 353.25 + 1130.4
SA = 1483.65 square feet!
 

Let's look at one more...


Jim has to paint a wooden dowel (a cylindrical piece of wood) that has a length (or height) of 36" and a diameter of 3".  What is the total surface area which Jim has to paint?
 

In this problem:
d = 3"
r = 1.5"
h = 36"
let pi = 3.14
SA = 2Π r2 + Π dh
SA = 2(3.14)(1.52) + (3.14)(3)(36)
SA = 14.13 + 339.12
SA = 353.25 square inches!
 

 For some more practice on your own....
Click here!