Using a Surface Integral for Mathematical Analysis of the Area of an Island

[daphnelee-mh]

Homework Statement

(Attached below)

Relevant Equations

A=sqrt[1+(dz/dx)^2+(dz/dy)^2]dA

I am not clearly understand what the question requests for, is it okay to continue doing like this ? Kindly advise, thanks

 

[scottdave]

Take a look at this link. I think you'll see how this relates to the shape of the island.
https://en.wikipedia.org/wiki/Spherical_cap

 

[LCKurtz]

The shape of the island is an upside-down paraboloid. The integral looks like everything is OK except the $r$ limits should be reversed. You want to integrate from the smallest to largest values of $r$ to get a positive answer.

 

[scottdave]

The shape of the island is an upside-down paraboloid. The integral looks like everything is OK except the $r$ limits should be reversed. You want to integrate from the smallest to largest values of $r$ to get a positive answer.

I believe you're right. I looked at it wrong.