Stewart – Calculus ET 8e Chapter 8 Form F
5. Find the area of the surface obtained by rotating the curve about the x-axis.
6. A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find the force
exerted by the water on the plate. (The weight density of water is 62.4 lb/ft3.)
(f
t
)
12345 x
1
–1
–2
–3
–4
y
(ft)
7. Use Simpson’s Rule with n = 6 to estimate the length of the curve , .
Round your answer to six decimal places.
____ 8. Find the area of the surface obtained by rotating the circle about the line .
Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 8 Form F
9. Dye dilution is a method of measuring cardiac output. If A mg of dye is used and c(t) is the
concentration of the dye at time t, then the cardiac output over the time interval [0, T ] is given by
Find the cardiac output over the time interval [0, 15] if the dye dilution method is used with mg
of dye and the dye concentration, in mg/L, is modeled by
,
where t is measured in seconds.
10. Find the area of the surface obtained by revolving the given curve about the x-axis.
on
____ 11. Find the length of the curve. Select the correct answer.
a.
b.
c.
d.
e.
12. Write an integral giving the area of the surface obtained by revolving the curve about the x-axis. (Do not
evaluate the integral.)
y = on [4, 6]
13. If the infinite curve , is rotated about the x-axis , find the area of the resulting surface.
Stewart – Calculus ET 8e Chapter 8 Form F
____ 14. Suppose the average waiting time for a customer’s call to be answered by a company representative
(modeled by exponentially decreasing probability density functions) is minutes. Find the median
waiting time. Select the correct answer.
a. minutes
b. minutes
c. minutes
d. minutes
e. minutes
15. You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force
exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)
5 ft
8ft
____ 16. You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force
exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)
Select the correct answer.
5ft
a. 5,200 lb
b. 1,040 lb
c. 520 lb
d. 2,600 lb
17. Find the centroid of the region bounded by the graphs of the given equations.
Stewart – Calculus ET 8e Chapter 8 Form F
18. A large tank is designed with ends in the shape of the region between the curves and ,
measured in feet. Find the hydrostatic force on one end of the tank if it is filled to a depth of ft with
gasoline. (Assume that the density of the gasoline is 42.0 lb/ .)
19. A hot, wet summer is causing a mosquito population explosion in a lake resort area. The number of
mosquitoes is increasing at an estimated rate of per week (where t is measured in
weeks). By how much does the mosquito population increase between the 4th and th weeks of
summer?
____ 20. The standard deviation for a random variable with probability density function f and mean µ is
defined
.
Find the standard deviation for an exponential density function with mean .
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 8 Form F
Stewart – Calculus 8e Chapter 8 Form F
Answer Section
Stewart – Calculus ET 8e Chapter 8 Form G
1. Find the length of the curve.
____ 2. Find the length of the curve. Select the correct answer.
a.
b.
c.
d.
e. None of these
3. Find the length of the curve for the interval .
4. Find the arc length of the graph of the given equation on the specified interval.
y =
2
3
(+ 1) , [3, 4]
5. Set up, but do not evaluate, an integral for the area of the surface obtained by rotating the curve
about the x-axis on the interval .
Stewart – Calculus ET 8e Chapter 8 Form G
____ 6. Find the area of the surface obtained by rotating the curve about the y-axis. Select the correct answer.
a.
b.
c.
d.
e. None of these
7. Find the area of the surface obtained by rotating the circle about the line .
8. Find the area of the surface obtained by revolving the given curve about the x-axis.
on
Stewart – Calculus ET 8e Chapter 8 Form G
____ 9. If the infinite curve , is rotated about the x-axis , find the area of the resulting surface.
Select the correct answer.
a.
b.
c.
d.
e.
10. You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force
exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)
5 ft
4ft
____ 11. A trough has vertical ends that are equilateral triangles with sides of length 4 ft. If the trough is filled with
water to a depth of 1 ft, find the force exerted by the water on one end of the trough. Round to one decimal
place. (The weight density of water is 62.4 lb/ft3.) Select the correct answer.
a. 12.0 lb
b. 249.6 lb
c. 6.0 lb
d. 499.2 lb
Stewart – Calculus ET 8e Chapter 8 Form G
12. The masses
are located at the points . Find the moments and and the center of mass of the
system.
;
13. A large tank is designed with ends in the shape of the region between the curves and ,
measured in feet. Find the hydrostatic force on one end of the tank if it is filled to a depth of ft with
gasoline. (Assume that the density of the gasoline is 42.0 lb/ .)
____ 14. A trough is filled with a liquid of density 855 kg/ . The ends of the trough are equilateral triangles with
sides m long and vertex at the bottom. Find the hydrostatic force on one end of the trough.
Select the correct answer.
a.
b.
c.
d.
e.
____ 15. Find the centroid of the region bounded by the given curves. Select the correct answer.
a.
b.
c.
d.
e.
16. A vertical plate is submerged in water (the surface of the water coincides with the x-axis). Find the force
exerted by the water on the plate. (The weight density of water is 62.4 lb/ft3.)
(f
t
)
12345 x
1
–1
–2
–3
–4
y
(ft)
Stewart – Calculus ET 8e Chapter 8 Form G
____ 17. Use the Theorem of Pappus to find the volume of the solid obtained by revolving the region bounded by the
graphs of and about the y-axis. Select the correct answer.
a.
8
b.
32
3
c.
4
d.
16
3
18. The marginal cost function is defined to be the derivative of the cost function. If the marginal
cost of manufacturing x units of a product is
(measured in dollars per unit) and the fixed start-up cost is , use the Total Change
Theorem to find the cost of producing the first 5,000 units.
____ 19. According to the National Health Survey, the heights of adult males in the United States are
(normally distributed with mean) 73 inches, and standard deviation of 2.8 inches. What is the
probability that an adult male chosen at random is between inches and inches tall?
Select the correct answer.
a. 0.5222
b. 0.7154
c. 0.6512
d. 0.5528
e.
f. 0.2812
20. Suppose the average waiting time for a customer’s call to be answered by a company representative
(modeled by exponentially decreasing probability density functions) is minutes. Find the median
waiting time.
Stewart – Calculus ET 8e Chapter 8 Form G
Answer Key
Stewart – Calculus ET 8e Chapter 8 Form H
____ 1. Find the length of the curve. Select the correct answer.
a.
b.
c.
d.
e. None of these
2. Find the length of the curve for the interval .
3. Use Simpson’s Rule with n = 6 to estimate the length of the curve , .
Round your answer to six decimal places.
4. Find the arc length of the graph of the given equation on the specified interval.
y =
2
3
(+ 1) , [2, 5]
5. Set up, but do not evaluate, an integral for the length of the curve.
6. Find the area of the surface obtained by rotating the curve about the y-axis.
Stewart – Calculus ET 8e Chapter 8 Form H
7. Write an integral giving the area of the surface obtained by revolving the curve about the x-axis. (Do not
evaluate the integral.)
y = on [3, 6]
____ 8. If the infinite curve , is rotated about the x-axis , find the area of the resulting surface.
Select the correct answer.
a.
b.
c.
d.
e.
9. You are given the shape of the vertical ends of a trough that is completely filled with water. Find the force
exerted by the water on one end of the trough. (The weight density of water is 62.4 lb/ft3.)
5 ft
7ft
10. A trough has vertical ends that are equilateral triangles with sides of length 7 ft. If the trough is filled with
water to a depth of 4 ft, find the force exerted by the water on one end of the trough. Round to one decimal
place. (The weight density of water is 62.4 lb/ft3.)
11. Find the centroid of the region bounded by the graphs of the given equations.
Stewart – Calculus ET 8e Chapter 8 Form H
____ 12. A large tank is designed with ends in the shape of the region between the curves and ,
measured in feet. Find the hydrostatic force on one end of the tank if it is filled to a depth of ft with
gasoline. (Assume that the density of the gasoline is 42.0 lb/ .) Select the correct answer.
a. 5,785 lb
b. 4,850 lb
c. 6,918 lb
d. 2,683 lb
e. lb
f. 3,855 lb
13. A trough is filled with a liquid of density 855 kg/ . The ends of the trough are equilateral triangles with
sides m long and vertex at the bottom. Find the hydrostatic force on one end of the trough.
14. Find the centroid of the region bounded by the given curves.
____ 15. Find the centroid of the region bounded by the given curves. Select the correct answer.
a.
b.
c.
d.
e.
16. Find the centroid of the region bounded by the graphs of the given equations.
Stewart – Calculus ET 8e Chapter 8 Form H
17. Dye dilution is a method of measuring cardiac output. If A mg of dye is used and c(t) is the
concentration of the dye at time t, then the cardiac output over the time interval [0, T ] is given by
Find the cardiac output over the time interval [0, 15] if the dye dilution method is used with mg
of dye and the dye concentration, in mg/L, is modeled by
,
where t is measured in seconds.
____ 18. The marginal revenue from producing x units of a certain product is
(in dollars per unit).
Find the increase in revenue if the production level is raised from 1,100 units to units.
Select the correct answer.
a. $37,974,583
b. $51,367,000
c. $26,866,667
d. $17,765,250
e. $
19. According to the National Health Survey, the heights of adult males in the United States are
(normally distributed with mean) 73 inches, and standard deviation of 2.8 inches. What is the
probability that an adult male chosen at random is between inches and inches tall?
____ 20. The manager of a fast-food restaurant determines that the average time that her customers wait for
service is 2 minutes. Find the probability that a customer is served within the first minutes.
Select the correct answer.
a.
b.
c.
d.
e.
Stewart – Calculus ET 8e Chapter 8 Form H
Answer Key