# Math Help - volume of half ball mmn 15 4a

1. ## volume of half ball mmn 15 4a

2. I suggest you switch to spherical coordinates as soon as possible. Review the section in your book on spherical coordinates. In particular, you should know how to describe half a sphere and that the Jacobian in spherical coordinates is $J(r, \theta, \varphi)=r^2\sin\theta$. In this case you'll have $0\leq \theta\leq \pi/2$ (assuming the ball is as you've graphed it).

Spherical coordinate system - Wikipedia, the free encyclopedia

3. i tried to solve it like this but i got a bad resolt where is my mistake?

4. Originally Posted by transgalactic
i tried to solve it like this but i got a bad resolt where is my mistake?
There is a miscommunication between the two of you. Mondreus is you theta as the azimuthal angle, but you are using phi as the azimuthal angle.

This is a common problem depending on which books you are reading

5. where is my mistake why i get 0

6. TheEmptySet told you where the error lies. I used the symbols from the Wikipedia article where a unit sphere is $0 < r < 1, 0 < \theta < \pi, 0 < \varphi < 2\pi$.

You have switched the limits for $\theta$ and $\varphi$.

7. i disagree
$0 < \varphi < \pi/2$
not 2 pi
correct?

8. I was referring to the unit sphere.

What you posted is only correct if the Jacobian for the spherical coordinates in this problem is $r^2\sin\varphi$. Again, read the Wikipedia article I linked to if you're confused about the symbols used.