• Support PF! Buy your school textbooks, materials and every day products Here!

Surface area of cap using integrals

  • Thread starter lilmul123
  • Start date
  • #1
40
0

Homework Statement


The question asks,

"Find the surface area of the cap cut from the sphere x^2+y^2+z^2=2 by the cone z = sqrt(x^2+y^2)" The answer should be 2pi(2-sqrt(2))

My main problem is not knowing how to get started.

Homework Equations



With the example given, it seems we need to find cos(v) first using the equation cos(v) = n*.k/|n|.

The Attempt at a Solution



I found the normal line to be 2xi+2yj+2zk. Using the above formula, I eventually reached the conclusion that z/sqrt(r^2+z^2). I don't know how to use this in an integral and it doesn't follow the example our professor gave us either. Can anyone help?
 

Answers and Replies

  • #2
104
0
Tame this problem by writing:

z = r cos (theta) (here theta is the zenith)

and

r^2 = x^2 + y^2 + z^2.

Work in spherical coordinates. It'll be that much easier.
 

Related Threads for: Surface area of cap using integrals

  • Last Post
Replies
3
Views
5K
Replies
1
Views
2K
Replies
7
Views
534
  • Last Post
Replies
5
Views
5K
Replies
2
Views
9K
Replies
1
Views
1K
  • Last Post
Replies
1
Views
3K
Replies
1
Views
3K
Top