Navigate back to the activity.

In spherical coordinates, some students started with an integral of “onion layers”, $\int 4 \pi r^{2} dr$, while others integrated over phi and theta. This made for an interesting discussion as we saw that both approaches give the same result, and discussed the ideas of solid angle and spherical symmetry.

Several students had some confusion over theta and phi (natural given the math/physics switch), which lead to confusion in the limits of integration - this can lead to some funny results.

Having a beach ball to point to and draw on was very helpful. A paper sphere-by-revolution would have been good too.