I see the problem, and my brain just freezes, i have no idea how to start on this problem, what is the general strategy?
assuming your in multivariable you’ll probably want to find the intersection of the two surfaces (x^2 + y^2=32). Then reparamaterize your sphere in terms of angles theta and phi r(theta,phi). then transform your domain of (x^2 + y^2=32) in terms of theta/Phi should be[02pi][0pi/4]. And finally integrate the magnitude of the cross product of the 2 partials of r(theta,phi) over your new theta/Phi domain. For the surface area problems in general you need to be able to do the reparamatarization into 2 variables and integrate the cross product deal over the correct domain thats about as simple as I can put it. If your still having trouble with it I would recomend staying off the SAMA thread for a couple hours till you can get it.
I appreciate the help bro, but how did you know that the domain in terms of phi would be pi/4?
from your paramatarization x=sqrt(64)sin(phi)cos(theta) y=sqrt(64)sin(phi)sin(theta) plug that into your domain x^2 +Y^2 =32 and it will give you the upper bound for your domain in phi
I’m stuck on the part where you have to find the magnitude of the cross product of r by theta crossed with r by phi, my cross product is so incredibly long that it takes up a whole page. What should i do?
The magnitude of your cross product = 64sin(phi), which takes about an entire page to prove so you can either spend the rest of the night proving it or do what I did and just write the result.
LOL brillient!
[quote]sig805 wrote:
The magnitude of your cross product = 64sin(phi), which takes about an entire page to prove so you can either spend the rest of the night proving it or do what I did and just write the result. [/quote]
I appreciate that man, but if it takes a whole page, then how did you know what it was? Did you use an online calculator? I certainly hope you didn’t sit there and calculate the answer by hand.
here is a quicker approach.
observe the line of the cones radial symmetry includes the spheres center.
then consider it in two dimensions z and r where r^2=x^2+y^2
now find the angle of intersection of the triangle with the circle.
the rest should sove itself.
if you get stuck a second time, try doing squats till failure.
[quote]jdinatale wrote:
[quote]sig805 wrote:
The magnitude of your cross product = 64sin(phi), which takes about an entire page to prove so you can either spend the rest of the night proving it or do what I did and just write the result. [/quote]
I appreciate that man, but if it takes a whole page, then how did you know what it was? Did you use an online calculator? I certainly hope you didn’t sit there and calculate the answer by hand.[/quote]
oh no of course I didn’t do it by hand I went out cooked my steaks and then looked in my old calculus book. But considering you’ll probably be integrating over spheres often its probably a good one to memorize also most graphing calculators can solve cross products.