- #1

Jim4592

- 49

- 0

## Homework Statement

Use spherical coordinates to find the volume of the solid that lies above the cone z

^{2}= x

^{2}+ y

^{2}and below the sphere x

^{2}+ y

^{2}+ z

^{2}= z

## Homework Equations

I'm going to use { as an integral sign.

Volume = {{{ P

^{2}Sin[Φ] dP dΦ dΘ

## The Attempt at a Solution

P

^{2}= x

^{2}+y

^{2}+z

^{2}

P

^{2}= z

P = Sqrt[z]

(P Cos[Φ])

^{2}= P

^{2}Sin

^{2}[Φ]

Cos

^{2}[Φ] = Sin

^{2}[Φ]

Tan

^{2}[Φ] = 1

Φ = Pi/4

And for the limits of integration i got:

from 0 to 2 Pi on the first integral bracket

from 0 to Pi/4 on the second integral bracket

from 0 to Sqrt[z] on the thrid integral bracket

I was hoping someone could please confirm that these are the right limits of integration before i evaluate it, thanks in advanced!