Calculus III: Sketching Solids with Spherical Coordinates

[acid_rain]

I really have difficulty with spherical coordinates graphings. can someone help me with this problem?

Sketch the solid consisting of all points with spherical coordinates (ρ,θ,φ) such that 0≤ θ ≤π/2, 0≤ φ ≤π/6, and 0≤ ρ ≤2cosφ

thanks so much!

i think this looks like a bowl with radius ρ= root 3,
then I don't understand how to graph theta and phi according to that range. that's where i got stuck.

 

[quasar987]

The "range" of ρ is dependant upon the value of φ. So if you start at φ=0. At this point, all the ρ btw 0 and 2 are permitted. But as φ progresses towards π/6, ρ can ony take value btw 0 and 2cosφ. And at φ=π/6, it can only take values btw 0 and \sqrt{3}. In btw, the range of rho decrease as cosφ decreases btw 0 and π/6, i.e. very slowly at the beginning (the crest of the cos) and then steadily until π/6.

Now that you've got the range of ρ and φ covered, just complete the volume by making θ vary.