MAT 146
Test #2r Part II
50 points (Part II: 30 points)
Impact on Course Grade: approximately 12.5%
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15. Determine the volume of the solid created when the region enclosed by the graphs of y = 0,
x = 1, x = 2, and y = –x2 is rotated about the line y = 2. In your solution, include:
 a sketch of the graph of the bounded region and a sketch of the solid of revolution,
 a sketch of a typical slice—and its dimensions—used in determining the volume,
 appropriate boundary points (limits of integration) and how you determined them,
 the integral used to calculate volume, and
 a numerical solution as a common fraction reduced to lowest terms.
16. The temperature T, in degrees F, for a given city is modeled by the function
t
T(t)  50  14 sin , where t is hours after 9 am.
12
(a) What is the average temperature during the time period from 9 am to 9 pm? Express your
solution as a decimal value rounded to the nearest thousandth of a degree.
(b) Determine a time k, between 9 am and 9 pm, so that the average temperature during the time
period from 9 am to k is 60º F. Express k as a decimal value rounded to the nearest thousandth of
an hour after 9 am.
17. The manager of a fast-food restaurant has determined that the average time her customers
wait for service is 3 minutes, so she has modeled the wait time with the probability density
function w(t) 
1 t
e , t  0, t in minutes.
3
1
3
(a) Determine the probability that a customer has to wait for more than 5 minutes at this
restaurant. Express this probability as a decimal value rounded to the nearest ten-thousandth of a
unit.
(b) Determine the probability that a customer is served within the first minute at this restaurant.
Express this probability as a decimal value rounded to the nearest ten-thousandth of a unit.
(c) The manager intends to advertise that any customer not served within a certain time period
will get a free sandwich. The manager, however, does not want to give away sandwiches to more
than 5% of her customers. What time period should the advertisement state? Express your
solution as a positive integer rounded to the nearest minute.
18. It has been documented that the heights of adult males in the United States are normally
distributed with mean 69.0 inches and standard deviation 2.8 inches.
(a) What is the probability that an adult male chosen at random is between 64 inches and 71
inches tall? Express this probability as a decimal value rounded to the nearest ten-thousandth of a
unit.
(b) What percent of the adult male population is more than 6’ 2” tall? Express this solution as a
percentage rounded to the nearest hundredth of a percentage point.
(c) What portion of the adult male population in the United States will be within 2.8 inches of
being 69.0 inches tall? Express this solution as a percentage rounded to the nearest hundredth of
a percentage point.
19) Choose ONE of the solids described below and use calculus to derive the given formula for
the volume of that solid. If more than one solution is shown, I will evaluate the first one I get
to.
(I) a sphere with radius r ( V 
4 3
r )
3
(II) a cone with base radius r and height h ( V 
1 2
r h )
3
(III) a pyramid with a square base (sides length s) and height h ( V 
1 2
s h)
3
Question
19 is
optional!
If you leave
this page blank,
I will use the
results for
question 19 of
the first version
of Test #2.
If the page is
not blank, I will
evaluate this
response to
question 19 and
use it in
determining
your score for
Test #2.
Calculus II
MAT 146
Test #2
Total Points:
Impact of Exam on Semester Grade:
50
Approximately 12.5%
Evaluation Criteria
Part I: No Calculators
20 points
Questions 1 through 10
1 point each with no partial credit. No need to show any work on these.
Questions 11 (2 points) and 12 (3 points)
Show all steps leading to each solution. Be clear, complete, and accurate.
Question 13: 2 points
Show all parts of the required set-up. Be clear, complete, and accurate.
Question 14: 3 points
Show all elements of the required volume representation.
Part II: Calculators Allowed
30 points
State any numerical solutions as exact values in rational expressions reduced to lowest terms. If
approximations are required, express as a decimal value rounded accurately to the nearest part
of a unit as stated below.
Questions 15: 5 points
1 point for each of the bulleted items. Be clear, complete, and accurate.
Question 16: 6 points
(a) 3 points, (b) 3 points: Show evidence to support each result; round each to nearest
thousandth; use appropriate units to label each solution.
Question 17: 6 points
(a) 2 points, (b) 2 points, (c) 2 points
Show evidence to support each result; round (a) and (b) to nearest ten-thousandth, round (c) to
nearest minute; use appropriate units to label each solution.
Question 18: 8 points
(a) 3 points, (b) 3 points, (c) 2 points
Show evidence to support each result; round (a) to nearest ten-thousandth, round (b) and (c) to
nearest hundredth of a percentage point.
Question 19: 5 points
1 point: Include a sketch or a graph to help illustrate the task.
2 points: Accurate set-up of the calculus used to represent the volume.
2 points: Accurate steps from set-up to completed justification of result.