How to Find the Volume of a Bounded Region with Sphere and Cone Equations

[HeheZz]

Homework Statement

Find the volume of a region bounded above by the unit sphere x^2+y^2+z^2=1 and below by the cone z=sqrt(x^2+y^2). I am really confuse here.. ><

Homework Equations

Sphere: x^2+y^2+z^2=1
Cone: z=sqrt(x^2+y^2)

The Attempt at a Solution

I had plot the graph of the sphere and cone and i am pretty confuse to use. Just want to have some help.

 

[The Chaz]

Volume requires a triple integral. How would you set this up? have you ever used polar/cylindrical/spherical coordinates?

 

[HeheZz]

Tea, i try using polar coordinates..

In the spherical, the equation of the sphere is r = 1

And the cone is rcosθ=√(r^2 sin^2 θ cos^2 φ + r^2 sin^2 θ sin^2 φ)=rsinθ

If we divide both sides by rcosθ, then we get

tanθ=1,θ=π/4

So, we have the triple integral:

∫0-2pi ∫0-(π/4) ∫0-1 (r^2 sinθdrdθdφ)

I am not sure if this is correct..