• Chapter 8 -- sections 8.2, 8.3 and 8.4 (in the old edition, sections 8.1, 8.2 and 8.3)

Fourth Homework Assignment - due at lecture on Tuesday, October 11.

1. Reading: Sections 8.2, 8.3 and 8.4 (old ed., sections 8.1, 8.2 and 8.3)
2. Textbook assignment: (submit nothing) Make certain you can do the following problems from the textbook:
• Section 8.2 (old ed., section 8.1), page 467 (old ed., page 459) # 3, 5, 11, 33, 45, 57 (old ed., #55)
• Section 8.3 (old ed., section 8.2), page 474 (old ed., page 466), #5, 15, 19, 23, 31, 37, 69
• Section 8.4 (old ed., section 8.3), page 479 (old ed., page 470), #3, 7, 15, 25, 35, 43, 55
3. Textbook assignment: Submit answers to Homework Assignment 4 on MyMathLab. If for some reason you are unable to access MyMathLab, the Assignment 4 problems correspond roughly to the following textbook problems, and if you need to, you can turn in solutions to the following textbook problems on paper at lecture on October 11:
• Section 8.2 (old ed., section 8.1), page 467 (old ed., page 459) # 4, 6, 12, 20, 32, 46, 56 (old ed., #54), 60 (old ed., #58), 62 (old ed., #60)
• Section 8.3 (old ed., section 8.2), page 474 (old ed., page 466), #8, 18, 22, 28, 44, 64, 72
• Section 8.4 (old ed., section 8.3), page 479 (old ed., page 470), #4, 8, 20, 32, 36, 52, 58

BONUS PROBLEM!!

Bonus problem #4: A cylindrical glass of radius r and height L is filled with water and then tilted until the water remaining in the glass exactly covers its base.

• (a) Determine a way to "slice" the water into parallel rectangular cross sections and then set up a definite integral for the volume of the water in the glass.
• (b) Determine a way to "slice" the water into parallel cross-sections that are trapezoids and then set up a definite integral for the volume of the water.
• (c) Find the volume of water in the glass by evaluating one of the integrals in part (a) or part (b).
• (d) Find the volume of water in the glass from purely geometric considerations.
• (e) Suppose the glass is tilted until the water covers half the base. In what direction can you "slice" the water into triangular cross sections? Rectangular cross-sections? Cross-sections that are segments of circles? Find the volume of water in the glass.
• Here are two pictures that may help:
  

For full credit, you must be as specific as you possibly can! When you have solved it, either write up the solution by hand and give it to me, or else send the solution to

deturck@math.upenn.edu

by electronic mail - extra credit for the first complete solution I receive.