The final exam in cumulative and is worth 25% of your final grade. This review only covers new material that we learned after the last midterm exam (Sections 6.2, 6.3, and 6.4). However, you are responsible for knowing all of the material learned this semester. This review will give you a good indication of the types of questions that you may be asked on the new material. Look at the old reviews and exams to study the old material.

Here is a list of things that you must know and understand from Sections 6.2-6.4:

- Find volume of a solid of revolution using the Disk/Washer Method and the Shell Method.
- Find arc length.
- Find surface area.

**Reminders:**
During the exam, SHOW ALL YOUR WORK and
JUSTIFY YOUR ANSWERS when necessary.
Also, be organized and neat!

Answer each of the following questions.

1.
Given the region bounded by
and
,
find the volume of the solid formed by revolving about the *x*-axis.

2.
Given the region
bounded by
and
,
find the volume of the solid formed by revolving the region about the *x*-axis.

3.
Given
and
,
find the volume of the solid formed by revolving about the *y*-axis.

4. Given , , and , find the volume of the solid formed by revolving the region about the line .

5. Find the arc length of the curve of the following function on the interval .

6.
Find the surface area of the solid formed by revolving the
following function about the *x*-axis
over
the interval
. (Kinda hardâ€¦but fun!)

7.
Find the surface area of the solid formed by revolving the
following function about the *y*-axis
over
the interval
.