onlystudents
Math 265 Name:
Fall 2014
Exam 3 (Version B)
11/7/2014
Time Limit: 50 Minutes Section
This exam contains 6 pages (including this cover page) and 9 questions.
Total of points is 100. Show all of your work for full credit.
Grade Table (for teacher use only)
Question Points Score
1 10
2 10
3 15
4 15
5 15
6 15
7 10
8 10
9 0
Total: 100
1. (10 points) Find the volume under z = 2 − x lying over the figure in the base plane
bounded by x = 0, x = 2, y = 0, and y = 4 − x.
, onlystudents
Math 265 Exam 3 (Version B) - Page 2 of 6 11/7/2014
2. (10 points) Change the order of integration for the following integral
Z2 Z4
f (x, y)dxdy
0 y2
3. (15 points) Consider the upper hemisphere x2 + y 2 + z 2 = 9 and z ≥ 0. Write the
integral (do not evaluate) which gives the volume of the sphere in
1. Cylindrical Coordinates
2. Rectangular Coordinates
3. Spherical Coordinates
Math 265 Name:
Fall 2014
Exam 3 (Version B)
11/7/2014
Time Limit: 50 Minutes Section
This exam contains 6 pages (including this cover page) and 9 questions.
Total of points is 100. Show all of your work for full credit.
Grade Table (for teacher use only)
Question Points Score
1 10
2 10
3 15
4 15
5 15
6 15
7 10
8 10
9 0
Total: 100
1. (10 points) Find the volume under z = 2 − x lying over the figure in the base plane
bounded by x = 0, x = 2, y = 0, and y = 4 − x.
, onlystudents
Math 265 Exam 3 (Version B) - Page 2 of 6 11/7/2014
2. (10 points) Change the order of integration for the following integral
Z2 Z4
f (x, y)dxdy
0 y2
3. (15 points) Consider the upper hemisphere x2 + y 2 + z 2 = 9 and z ≥ 0. Write the
integral (do not evaluate) which gives the volume of the sphere in
1. Cylindrical Coordinates
2. Rectangular Coordinates
3. Spherical Coordinates
