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**lllll** Given a cone $\displaystyle z=\sqrt{x^2+y^2}$ and a sphere $\displaystyle x^2+y^2+z^2=1$, find the area above the cone and under the sphere.

I figure if I convert this into polar coordinates it will simplify the calculations, so I'll have $\displaystyle 0 \leq r \leq 1$ for the radius since $\displaystyle x^2+y^2+z^2=1$. Now for the angles, I'm not 100% sure, but I would imagine that they're in a $\displaystyle \frac{\pi}{4}$ neighborhood on the xz and yz planes, but if we consider the xy plane then this will just be a circle centered at 0 with radius 1.

I figure I'll have:

$\displaystyle \iint_D \sqrt{x^2+y^2} dA = \int \int_0^1 \sqrt{r^2} \cdot r \ dr \ d\theta = \int \int_0^1 r^2 \cdot \ dr \ d\theta$ but without the values for $\displaystyle \theta$, I can't continue.