Although there are many uses for finding out the area of a cylinder (most having to do with school work) the only one I could think of was for finding out the displacement of a liquid.
So there are four (4) parts to finding out the surface area of a cylinder.
Surface area will now be known as the letter X. (Surface area = X)
The formula we will be using is 2(pi r 2) + (2 pi r)* h = X
Step 1: First Step...
The first of the steps involves breaking down the parts of a cylinder.
You have both the top and the bottom of the cylinder and the side.
The top and the bottom would be 2 circles of the same size.
Cut the left over tube to create a rectangle.
Step 2: Second Step...
We will use the equation in the picture below.
X is the area of the circle which we are trying to find is this step.
That thing that looks like two T's stuck together is called pi.
pi is the ratio of the circumference to the diameter of a circle. Pi is approximately equal to 3.14159265358979323846.
For this Instructable and also for most common uses pi is equal to 3.14.
Now for the r.
r refers to the radius of the circle. The radius is the measured distance from the center to the edge of the circle.
For this Instructable that number will be 7 (the wife gave me a random number :P)
The equation now looks like this:
That little 2 up there next to the r in the picture means that you square the r. Squaring is where you multiply the number to its self (I can't seem to make the little 2 stay up here in the text so I am suplimenting the little 2 for (squared)). Since r=7 you square 7 (7x7) which equals: 49
OK this is what you have so far:
multiplying 3.14 by 49 and you get: 153.86
Your equation is now:
The surface area of the circle (X) equals 153.86un(squared) or units squared meaning they could be inches squared, feet squared, meters squared, etc. you just always put the 2 on it to signify that the number is the area of something)
OK next step is finding the area of a rectangle.
Step 3: Third Step...
The only problem that we face is we need to find the circumference of the circle in the last step first because that is one of the sides of the rectangle we are finding the area of.
The equation we will use for that is:C=TTd
C is the circumference
The 2 T's is pi
and the d is the diameter of the circle.
In the last step we learned that r or the radius was 7. To find the diameter just multiply the radius by 2.
The equation now looks like this:
C=pi x 14
Now pi is equal to 3.14 so next you multiply 3.14 by 14.
So now we know that the circumference equals 43.96 units
since the curcumferance is 43.96un we are going to put that at the top of our rectangle. (Remember that we got the rectangle from "cutting" the tube on one side and spreading it out)
We are going to put the measurement 312un on the other side because that is how tall the cylinder is. (again another random number I was given by my wife.)
(Use the picture for the next section)
To find the area of a rectangle we will use the equation:
X is the area of the rectangle
B is for the base (top and bottom) =43.69un
H is for the height =312un
So our equation looks like this:
Do the math and you get:
the surface area of the rectangle is 13,631.28un(squared).
Step 4: Fourth and Final Step...
Or just the area of our lovely cylinder.
Do you remember the area of the circles? It was:
153.86 units squared
And the area of the rectangle?
13,631.28 un squared
Now because there is a top and bottom to the cylinder you need to add the area of the circles twice and the rectangle once.
The equation looks like this:
(Again X is a representation of the area of the cylinder)
Now do the math........
The cylinder has a surface area of 13,939 units squared.
(remember units can be changes to anything and this number is squared because it is the area of something.)
Again all this was just a break down of the formula 2(pi r 2) + (2 pi r)* h = X
Hope this helped.
(Disclaimer: This is my first Instructable. Please be gental)