Find the volume of the portion of the unit sphere which lies inside the right circular cone having its vertex at the origin and making an angle $w$ with the positive z-axis.
Please help me with the sum. I understood that the area would look somewhat like an ice cream cone but how to use triple integration not understanding.
The volume can be integrated in spherical coordinates as
$$\int_0^{2\pi}\int_0^\omega \int_0^1 r^2\sin\theta \>dr d\theta d\phi=\frac{2\pi}3(1-\cos\omega)$$