Question

Using spherical coordinates, find the volume of the solid
inside $$z = (x^2 + y^2)^(1/2) $$
and bounded by $$ z^2 + x^2 + y^2 = 1, and z^2 + x^2 + y^2 = 4 $$

Answer 1

\[ \int_0^{2\pi} \int_0^{\frac{\pi}{4}} \int_1^2 \rho^2 \sin \phi \ d\rho\ d\phi \ d\theta = \frac{7\pi ( 2 - \sqrt{2})}{3} \]