Math C056
Exam 4
Fall Semester 2009
Questions 1 and 2 pertain to the following situation: A sphere has a 6.425-inch diameter.
1. Compute its surface area.
a. 518.75 in2 b. 129.69 in2
c. 329.21 in2
d. 42.98 in2
e. 17.65 in2
2. Compute its volume.
a. 43.23 in3
b. 138.87 in3
c. 68.53 in3
d. 79.08 in3
e. 110.36 in3
3. A firm manufactures lampshades in the shape of hemispheres with a 14.0-inch
diameter. The cost of the shade material is $0.60 per square foot. Compute the total
material expense of 2,500 lampshades.
a. $6,414.09
b. $599.95
c. $12,500.00 d. $95.75
e. $3,207.04
4. A hollow glass sphere has an outside circumference (great circle) of 23.80
centimeters. The wall thickness of the sphere is 0.50 centimeter. Compute the
weight of the sphere. Glass weighs 1.5 grams per cubic centimeter.
a. 32.57 gm
b. 41.86 gm
c. 19.06 gm
d. 76.49 gm
e. 118.16 gm
Questions 5 and 6 pertain to the following situation. A wooden planter is shown below.
The top section is in the shape of a prism with a square base. The bottom section is in the
shape of a frustum of a pyramid with square bases.
5. Compute the number of cubic feet of soil that can be held by the planter when full.
Disregard the thickness of the lumber.
a. 3.58 ft2
b. 19.44 ft3
c. 7.83 ft3
d. 11.46 ft3
e. 1.62 ft3
6. Compute the total number of square feet of lumber required in the construction.
Disregard the thickness of the lumber. Allow 15% for waste.
a. 6.62 ft2
b. 952.88 ft2
c. 4.98 ft2
d. 5.71 ft2
e. 7.61 ft2
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7. Compute the number of cubic yards of asphalt required to pave the section of land in
the figure below. The average thickness of the asphalt is 3.0 inches.
a. 217.76 yd3
b. 653.28 yd3
c. 147.95 yd3
d. 70.27 yd3
e. 97.44 yd3
c.
m:adjacent
f:hypoteneuse
b:opposite
d.
m:opposite
f:adjacent
b:hypoteneuse
e.
m:hypoteneuse
f:adjacent
b:opposite
8. Name sides m, f, and b.
a.
m:hypoteneuse
f:opposite
b:adjacent
b.
m:adjacent
f:opposite
b:hypoteneuse
9. State the ratio of each of the six trig functions in relation to
a.
sin
cos
tan
csc
sec
cot
1 = s/m
1 = t/m
1 = s/t
1 = m/s
1 = m/t
1 = t/s
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b.
sin
cos
tan
csc
sec
cot
1 = t/s
1 = m/s
1 = t/m
1 = s/m
1 = s/t
1 = m/t
c.
sin
cos
tan
csc
sec
cot
1 = m/s
1 = t/s
1 = s/t
1 = s/m
1 = m/t
1 = t/m
d.
sin
cos
tan
csc
sec
cot
1.
1 = s/t
1 = s/m
1 = t/s
1 = t/m
1 = m/t
1 = m/s
e.
sin
cos
tan
csc
sec
cot
1 = t/m
1 = s/m
1 = s/t
1 = m/t
1 = t/s
1 = m/s
10. Determine cos 40.495º.
a. 0.975
b. 0.712
c. 0.760
d. 0.866
e. 0.50
11. Determine tan 89º12′59″.
a. Undefined b. 0
c. 73.11
d. 4.96
e. 0.729
12. Determine csc 65º.
a. 0.906
b. 4.76
c. 0.251
d. 1.10
e. 69.44
13. Determine the value of angle A in decimal degrees if sin A = 0.79363.
a. 60.00º
b. 23.19º
c. 46.89º
d. 52.53º
e. 39.02º
14. Determine the value of angle A in decimal degrees if cos A = 0.98994.
a. 8.13º
b. 21.36º
c. 14.66º
d. 68.14º
e. 83.92º
15. Determine the value of angle A in decimal degrees if cot A = 4.86731.
a. 78.39º
b. 61.22º
c. 11.61º
d. 36.80º
e. 17.93º
16. Determine the value of angle A in decimal degrees if A = arcsin 0.7931.
a. 10.91º
b. 35.61º
c. 48.95º
d. 71.33º
e. 52.48º
17. Determine the value of angle A in decimal degrees if A = cot-1 4.2156.
a. 76.66º
b. 13.34º
c. 23.92º
d. 89.54º
e. 4.22º
18. Determine the value of angle A in degrees and minutes if cos A = 0.09561.
a. 22º56.71′
b. 84º30.81′
c. 17º35.86′
d. 56º21′
e. 34º18.52′
19. Determine the value of angle A in degrees and minutes if tan A = 7.06072.
a. Undefined b. 1º2.25′
c. 51º4.78′
d. 39º2.27′
e. 81º56.33′
20. Determine the value of angle A in degrees and minutes if cot A = 0.17976.
a. 42º12.76′
b. 15º18.92′
c. 79º48.56′
d. 54º21.50′
e. 82º71.23′
21. Determine the value of angle A in degrees and minutes if A = arccos 0.7931.
a. 17º42.11′
b. 37º31.43′
c. 68º36.71′
d. 49º8.41′
e. 82º12.96′
22. Determine the value of angle A in degrees and minutes if A = csc-1 4.3286.
a. 76º69.57′
b. 47º12.84′
c. 27º16.97′
d. 68º2.38′
e. 13º21.43′
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Use the following diagram to anwer questions 23, 24, and 25.
23. When
a. r
1 0 , what is the value of side y?
b. 0
c. 1
d. Undefined
e. x
24. When side x = side y, what is the value of the tangent function?
a. 0
b. Undefined c. 0.866
d.
e. 1
25. When side x = side r, what is the value of the secant function?
a. Undefined b. 1
c. 0
d. 0.50
e. 0.707
26. Write the cofunction of the complement of the angle for cos 81º.
a. sin 9º
b. sin 81º
c. tan 81º
d. cos 9º
e. sec 9º
27. Write the cofunction of the complement of the angle for sec 25º.
a. cos 65º
b. cot 65º
c. csc 65º
d. csc 25º
e. cos 25º
28. Write the cofunction of the complement of the angle for sin 51.88º.
a. csc 38.12º
b. cos 38.12º c. cos 51.88º d. tan 19.72º
e. sin 38.12º
29. Determine
a. 23.89º
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A in the following diagram.
b. 38.69º
c. 15.24º
d. 71.58º
e. 89.00º
30. Determine side x in the following diagram.
a. 6.77 cm
b. 0.998 cm
c. 0.148 cm
d. 3.58 cm
e. 5.20 cm
d. 4.571 in
e. 9.772 in
31. Determine side c from the following diagram.
a. 0.170 in
b. 7.624 in
c. 5.894 in
Questions 32, 33, and 34 pertain to the following diagram.
32. Determine 2 .
a. 9.870º
c. 80.13º
d. 71.30º
e. 24.57º
33. Determine side a.
a. 9.349 cm
b. 7.214 cm
c. 24.57 cm
d. 9.870 cm
e. 5.422 cm
34. Determine side b.
a. 3.164 cm
b. 9.870 cm
c. 9.349 cm
d. 3.341 cm
e. 5.228 cm
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b. 18.70º
35. A surveyor wishes to determine the height of a tower. The transit is positioned at a
distance of 200.00 feet from the foot of the tower. An angle of elevation of 46º50′ is
read in sighting the top of the tower. The height from the ground to the transit
telescope is 5′5″. What is the height of the tower?
a. 213.22′
b. 158.34′
c. 392.67′
d. 100.00′
e. 218.64′
36. The horizontal distance between 2 points that are located at different elevations is to
be determined. A surveyor positions the transit at a point that is 24.50 meters lower
than the second point. The height from the ground to the transit telescope is 1.80
meters. The second point is sighted, and 42.60º angle of elevation is read. What is
the horizontal distance between the two points?
a. 41.26 m
b. 18.50 m
c. 10.01 m
d. 38.72 m
e. 24.69 m
Questions 37 and 38 pertain to the following diagram.
A
X
B
37. Compute X .
a. 75.21º
b. 81.27º
c. 76.36º
d. 45.93º
e. 52.15º
38. Compute AB.
a. 3.86 m
b. 4.14 m
c. 4.52 m
d. 3.98 m
e. 4.05 m
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39. Compute the distance across centers, dimension D, of the holes in the locating plate in
the figure below.
a. 47.70 mm
b. 52.30 mm
c. 95.40 mm
d. 60.00 mm
e. 30.00 mm
40. Compute check dimension x of the external half of a dovetail slide shown below.
a. 5.630 in
b. 5.750 in
c. 6.631 in
d. 7.092 in
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e. 8.002 in