Problems 1-3 are related to Example 3.
1. Consider that part of the sphere x2 + y2 + z2 = a2 between the planes z = h1 and z = h2, where 0 ( h1 2. Show that the polar cap (Figure 9) on a sphere of radius a determined by the spherical angle ( has area 2((2(1 - cos().

3. Another Old Goat Problem Four goats have grazing areas A, B, C. and D, respectively. The first three goats are each tethered by ropes of length b, the first on a flat plane, the second on the outside of a sphere of radius a, and the third on the inside of a sphere of radius a. The fourth goat must stay inside a ring of radius b that has been dropped over a sphere of radius a. Determine formulas for A, B, C, and D and arrange them in order of size. Assume that b