5. Practice at home: Re-do the integrals in problems 1 and 4 using spherical coordinates. Make sure you get the same numerical answers as when you did the calculations in cylindrical coordinates.

6. Practice at home: Use spherical coordinates to find the area of the part of the sphere x 2 + y 2 + z 2 = 16 that lies above the plane z = 2. Then find the mass of that surface if the density is given by = z.

Problem 1 as referred to in 5 has already been done, problem 4 has not been done, and has been posted below the picture of 5 and 6. Please do both parts, thank you!

5. Practice at home: Re-do the integrals in problems 1 and 4 using spherical coordinates. Make sure you get the same numerical answers as when you did the calculations in cylindrical coordinates. 6. Practice at home: Use spherical coordinates to find the area of the part of the sphere r + y2 + 2 = 16 that lies above the plane z = 2. Then find the mass of that surface if the density is given by p= z. 4. Suppose the surface of problem 1 has a variable density of p(x, y, z) = V4 - 24. Find its total mass. Assume the units of mass are grams, and the units of distance are meters. (a) What are the units of p? (b) In the previous problem, we calculated the area of a patch as r. x re Ar A0 = 5rAr 10 . (c) What is the mass of a patch? (d) Integrate to find the total mass. 5. Practice at home: Re-do the integrals in problems 1 and 4 using spherical coordinates. Make sure you get the same numerical answers as when you did the calculations in cylindrical coordinates. 6. Practice at home: Use spherical coordinates to find the area of the part of the sphere r + y2 + 2 = 16 that lies above the plane z = 2. Then find the mass of that surface if the density is given by p= z. 4. Suppose the surface of problem 1 has a variable density of p(x, y, z) = V4 - 24. Find its total mass. Assume the units of mass are grams, and the units of distance are meters. (a) What are the units of p? (b) In the previous problem, we calculated the area of a patch as r. x re Ar A0 = 5rAr 10 . (c) What is the mass of a patch? (d) Integrate to find the total mass