Hello

I am trying to find the volume the region above the cone $\displaystyle z=\sqrt{x^2+y^2}$ and below the sphere $\displaystyle x^2+y^2+z^2=1$

I was told to consider the difference $\displaystyle z=\sqrt{x^2+y^2} - \sqrt{1-(x^2+y^2)} $

and to set the two equations equal to each other to get bounds

$\displaystyle \sqrt{x^2+y^2}=\sqrt{1-(x^2+y^2)}$

simplifies to

$\displaystyle x^2+y^2 = \frac{1}{2}$

so

$\displaystyle 0 \leq \theta \leq 2\pi$

and

$\displaystyle 0 \leq r \leq \frac{1}{\sqrt{2}}$

I can easily set up the integral from here. But I don't understand the geometry behind these steps. Could someone explain to me please?