- #1
forestmine
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Homework Statement
Find the volume enclosed by the spherical coordinate surface ρ = 2sin∅
Homework Equations
dV = ∫∫∫(ρ^2)sin∅dρd∅dθ
The Attempt at a Solution
(Sorry about my notation!)
Alright, here's what I've done so far...
Since the region is a torus, centered around the z-axis, I began by finding my limits of integration for ρ, which I think would simply be from 0 to 2sin∅.
For my limits for ∅, I started at the utmost point on the positive z-axis, which I believe is 0 in regards to ∅, and it covers the entire ∅ "region" down to the negative z axis, so the limits are 0 to pi.
And for θ, I got simply 0 to 2pi.
Given those limits, integrating ((ρ^2)sin∅)dρd∅dθ, I wind up with 0, which on the one hand, I've convinced myself makes sense, since it is a torus, and it is symmetrical about the axes (like saying the area under the cosine from 0 to 2pi is 0). On the other hand, a volume of 0 for a physical object simply doesn't make sense.
I have a feeling I'm simply going about the limits wrong. If I've got those right, I'll post my integration work in case someone can spot the problem.
Thanks guys!