- #1
Feodalherren
- 605
- 6
Homework Statement
Find the area of the part of the sphere x^2 + y^2 + z^2 = 4z
that lies inside the paraboloid x^2 + y^2 = z
Homework Equations
The Attempt at a Solution
I solved for the intercepts and found that they are z=0 and z=3.
The sphere is centered two units in the z-direction above the origin.
Hence I wanted to switch to spherical coordinates and got:
0≤Θ≤2∏
ρ=2
Now, since we know that the sphere is centered on (0,0,2) we can take find the angle from the Z axis easily.
(∏/3)≤Φ≤∏.
The Surface Area of this portion of the sphere should then become
[itex]\int^{2∏}_{0} \int^{∏}_{∏/3} 4SinΦ dΦdΘ[/itex]
[itex]
\int^{2∏}_{0} \int_{∏/3}_{∏} 4SinΦ dΦdΘ
[/itex]
I get 12∏, which is incorrect. The correct answer is 4∏. Where am I going wrong?
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