Surface area and total area

In summary: Every post criticzing spelling will have a typo. Every one criticizing grammar will have a mistake. And apparently every one upholding mathematical rigor will be cursed with a blunder.To err is human...But to really screw things up takes a computer!Originally posted by Tom MattsonBut to really screw things up takes a computer!I thought that was a tape measure... :)In summary, the difference between surface area and total area depends on the context of the question. In the case of a cylinder, the surface area refers to the lateral surface area while the total area refers to the sum of the lateral surface area and the area of the top and bottom faces. The formula for the surface area of a cylinder is 2π
  • #1
Integral0
49
0
What's the difference b/w surface area and total area? For example, the surface area of a cylinder is A = 2 pi rh while the total area of a cylinder is A = 2 pi rh x 2 pi r^2.

Thanks for the help =)
 
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  • #2
There is no difference between "total area" and "surface area" and your assertion that the "surface area" of a cylinder is 2pi rh is incorrect. That is the "lateral surface area". The ends of a cylinder are as much "surface" as the lateral surface.
 
  • #3
RE

not according to my math book.
 
  • #4
I guess by "surface area" your math book, as HallsofIvy said, means lateral surface area and by "total surface area" it means surface area. And this is not correct:
A = 2 pi rh x 2 pi r^2
it should be: A=2rπh + 2πr2. Why would you multiply the lateral surface area by the area of the top and bottom?

It would be pretty ridiculous if your math book called lateral surface area, "surface area" because no one will know what the heck you mean if you call it that.

-HBar
 
  • #5
What does n represent in your areas?
 
  • #6
Originally posted by Integral0
What does n represent in your areas?
It isn't N it is pi, done like this, & pi ; (minus the spaces) go back to General math, (the thread listing) and at the top you too can find "making math symbols" π
 
  • #7
RE

According to my SAT math book ->

"The surface area, A, of the side of the cylinder is the circumference of the circular base times the height: A = 2nrh. The area of the top and bottom are each nr^2, so the total area of a can is given by the formula A = 2nrh + 2nr^2"

So if you are eager to refute this, go right ahead! I am not mad or attempting to fight your opinions, instead, I am trying to see who is right and who is wrong . . . so -> I can do the problems right!

So please, tell me what's wrong with the statement above . . . its exactly what the book says about total area and surface area.

If the author is wrong . . . talk to Sharon Weiner Green and Ira K. Wolf from Barron's.
 
  • #8
oops!

I just noticed from HBAR a mistake that I had made when typing in the total area (I didn't mean to multiply 2nrh x 2nr^2, in reality, I meant to put a positive sign.

Thanks HBAR
 
  • #9
The surface area, A, of the side of the cylinder ...

Emphasis mine.
 
  • #10
The surface area, A, of the side of the cylinder is the circumference of the circular base times the height: A = 2nrh. The area of the top and bottom are each nr^2, so the total area of a can is given by the formula A = 2nrh + 2nr^2"

No, this is completely correct, but it is NOT what you initially said. You said " For example, the surface area of a cylinder is A = 2 pi rh while the total area of a cylinder is A = 2 pi rh x 2 pi r^2."

Your book says "the surface area of the SIDE of the cylinder" which is not the same as the "surface area of a cylinder".
(Sorry, Hurkyl, I just noticed you had already said this.)

Before you complain about your textbook, read it CAREFULLY.

Mathematics is very, very precise.

(I have friends who remark on how "anal" mathematicians are. Of course,they are generalizing from a very small sample!)
 
  • #11
Depends on the context of the question... The surface area may be the area of one side of a cube, whereas the net area may be the sum of the four sides of the cube.
 
  • #12
Originally posted by quantum
...the four sides of the cube.
How many sides on a cube?

Sorry, couldn't let it go following a post about how precise math is/has to be.
 
  • #13
Every post criticzing spelling will have a typo. Every one criticizing grammar will have a mistake. And apparently every one upholding mathematical rigor will be cursed with a blunder.

To err is human...
 

1. What is the difference between surface area and total area?

Surface area refers to the measurement of the exposed area of an object's outer surface, while total area includes both the surface area and any hidden areas, such as the inside of a hollow object.

2. How is surface area calculated?

Surface area is calculated by adding up the areas of all the individual surfaces of an object. For example, the surface area of a cube is found by multiplying the length of one side by itself, and then multiplying that value by six (since a cube has six equal sides).

3. Why is surface area important in science?

Surface area is an important measurement in science because it can affect how quickly a substance can absorb or release heat, how much friction an object experiences, and how much area is available for chemical reactions to occur.

4. How does surface area affect the rate of reaction?

The greater the surface area of a substance, the more area is available for reactants to come into contact with each other. This increases the chances of successful collisions and can lead to a faster rate of reaction.

5. What are some real-life examples of how surface area and total area are used?

Surface area and total area are used in a variety of everyday applications, such as determining the amount of paint needed to cover a wall, calculating the amount of wrapping paper needed for a gift, and designing more efficient heat exchangers in industrial processes.

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