Math 1B
Project # 2
20 Points
Due Date: Friday 26 February
NAME
Volumes
This project may be done in groups of 2 – 4 students. Each group will submit only one set of
solutions but each group member is expected to contribute. Please show all work on separate
sheets of paper and staple this page to the front.
I. Region R is bounded by y = x , x = 4 , and y = 0 . Set up the integral necessary to find the
volume of the solid if R is revolved about:
(8 points)
a)
b)
c)
d)
e)
f)
g)
h)
The x- axis using the Disk/Washer Method
The x- axis using the Shell Method
The y- axis using the Disk/Washer Method
The y- axis using the Shell Method
The line x = −2 using the Disk/Washer Method
The line x = −2 using the Shell Method
The line y = 5 using the Disk/Washer Method
The line y = 5 using the Shell Method
You do not need to integrate but I want to see a clear drawing with a typical disk, washer,
or shell.
II. Construct a model.
(12 points)
The model must meet the following requirements:
•
•
•
•
•
Label the coordinate axes
Show the region used to make the solid
Show the three dimensional shape of the solid
Show at least three basic disk/washer or shell sections
Neatness
1 points
3 points
3 points
3 points
2 points