# Surface area

ok why does

surface area = ( y) ( 1+ f ' (x)^(2) )^(1/2)

equal

surface area = (x ) (1+ f ' (x)^(2) )^(1/2)

the simplest explanation please.

## Answers and Replies

Defennder
Homework Helper
Where did you get those formulae from? And surface area of what? You're supposed to do a surface integral in 3D space (the details of which depend on the parametrisation of the surface area)to get the surface area, but I don't see any integral sign. The formulae you gave resembles the one given for arc length calculation.

For a surface area of a function in 3D, for which the surface z(x,y) is given, the surface area of the portion that projects down onto a region R is given by $$\int \int_R \sqrt{\left(\frac{\partial z}{\partial x} \right)^2 + \left(\frac{\partial z}{\partial y}\right)^2 + 1} \ \ dA$$

HallsofIvy
Science Advisor
Homework Helper
ok why does

surface area = ( y) ( 1+ f ' (x)^(2) )^(1/2)

equal

surface area = (x ) (1+ f ' (x)^(2) )^(1/2)

the simplest explanation please.

There can be no explanation- what you have written makes no sense at all! Are there supposed to be integrals in there?
Are you talking about the area of surfaces of rotation?

yes! in rotation! sorry i didnt know how to put an integral sign.