I was working on this problem and I
understand the boundaries for rho, and theta, when I see the vertex at the
origin is 90* I want to set my boundaries from 0 to pi/2. I'm not positive
why it's required to set from 0 to 45* unless it's because the picture
show's only the 45* region shaded in? Thank you again for extending the
homework assignment :)
Thank you,
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This question is meant to confuse you, which it did. Remember that φ is measured from the z-axis, which is poking out of the middle of ice cream on top of the cone. The confusion arises because the problem invites you to pay attention to the angle from one side of the cone to the opposite side of the cone--that is 90*--and oh by the way don't pay any attention to the fact that those two opposite sides have values of θ that are 180* apart. Instead of paying attention to that you should be paying attention to the angle between the z-axis and some radial line passing through the origin and going along the side of the cone somewhere--this will be at some fixed θ because you only go to one side of the cone--and this angle can only be 45*=90*/2
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