How Do Surface Area and Total Area Differ in Geometry?

[Integral0]

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 =)

 

[HallsofIvy]

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.

 

[Integral0]

RE

not according to my math book.

 

[HBar]

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

 

[Integral0]

What does n represent in your areas?

 

[Mr. Robin Parsons]

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

 

[Integral0]

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.

 

[Integral0]

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

 

[Hurkyl]

The surface area, A, of the side of the cylinder ...

Emphasis mine.

 

[HallsofIvy]

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!)

 

[quantum]

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.

 

[russ_watters]

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.

 

[selfAdjoint]

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...