Topics from Geometry
Perimeter, Area, and Volume
Dr. Robert J. Rapalje, Retired
Seminole State College of Florida
Sanford, FL 32773
NOTE: The following
exercises, #41 - 48, are perimeter, area, and volume applications from
the College Level Academic Skills Test (CLAST) Study Guide for the
Mathematics Subtest (1994) and the CLAST Item Specifications Sample Problems
(1990), State of Florida, Department of State.
41.
The figure below shows a water 42. The figure below
shows a running track
tank in the shape of a
cylinder having the shape of a rectangle with
with a hemi sphere on top.
If the semicircles at each end. If the width of
radius of the
cylinder is r and the the rectangle is 2y and the
length is 3x,
height is h, find the volume
of the tank. find
the distance around the track.
43. A patio is to be
built of concrete. The base of the patio is to be a slab of concrete 15
feet long by 12 feet wide by 6 inches thick. If one cubic yard of concrete
costs $39, how much will the concrete for the patio cost?
A. $65 B.
$130 C. $1560 D. $3510
44. A fence that costs
$6.50 per yard is to be placed around a rectangular yard that is 90 feet by
120 feet. What is the total cost of the fence?
A. $910 B.
$1365 C. $2730 D. $7800
45. A rectangular flower
bed measures 5 feet by 54 inches. The outside dimensions of a path around
the bed are 7¼ feet by 81 inches.
What is the area of the path?
A. 29 sq feet B.
317 sq feet C. 317.25 sq feet D. 3807 sq inches
46. The trunk of a tree
has a 1.2-meter diameter. What is its circumference?
A. 0.36 π sq meters
B. 0.6
π meters C. 1.2 π meters D. 1.44 π sq meters
47. What will be the cost
of carpeting an office that measures 12 feet by 15 feet if the carpet costs
$12.50 per square yard?
A. $250 B.
$650 C. $750 D. $2250
48. The outside
dimensions of a picture frame are 2 feet by 30 inches. If its outside
dimensions are 1¾ feet by 27 inches,
what is the area of the frame?
A. 12 sq feet B.
12.75 sq feet C. 153 sq inches D. 162 sq inches
Additional Exercises
Construction
49. You've been asked to participate in a Habitat for Humanity project in
a lower socio-economic community. The community is asking to make
improvements for children and families in a local park. You are
working with a team of people and they have given you the assignment of
designing and constructing a gazebo. You've decided to build the
gazebo in the shape of a hexagon. Find the length of each side if the gazebo
is to be 20 feet across (from side to side).
50. Does it make a difference if the gazebo described in #1 is to be 20
feet across (from corner to corner) instead of from side to side? Is this
design larger or smaller? Find the length of each side of the gazebo
according to this construction.
51. Concrete blocks are 8"x8"x16". How many blocks will it
take to build a wall that is 20 feet long and 10 feet high?
52. Concrete blocks cost $1.50 each, and labor for laying the blocks is
$1 each for the first 100 blocks and $.75 for each block thereafter. How
much will it cost for blocks and labor to build a wall that is 20 feet long
and 10 feet high? (See previous exercise.)
53. Wooden fence comes in prefabricated 8-foot lengths, costing $21.95
per unit. If a rectangular back yard is 40 feet on the sides and 100 across
the back, how many units will it take to fence both sides and the back of
the yard? If a post is required at each corner and between each unit, how
many posts will be required? If the posts cost $7.95 each, what is the total
cost of the prefabricated units and posts for the fence?
54. A 4-foot sidewalk, 6 inches thick, is to be built from the dining
room to a dormitory, a distance of a quarter mile. How many cubic yards of
concrete will be needed for the job?
Interior Design.
55. A rectangular room is 12 feet by 15 feet. How many square yards of
carpet will be needed to cover the floor?
56. A rectangular room is 12 feet by 15 feet, with 10 foot ceiling. If
paint can be applied at the rate of 300 square feet per gallon, how many
gallons of paint will be needed to paint the walls of the room (for
simplicity sake, neglect windows and doors)?
57. If the rectangular room in the previous exercise has 4 windows that
are each 6 feet by 8 and 2 doorways that are each 4 feet by 8 feet, does
this reduce the number of gallons of paint that you will need to paint the
room?
Agriculture.
58. A privacy hedge is to be planted, with one bush every 5 feet. If the
hedge must extend for a total distance of 300 yards, how many bushes will be
needed? If the bushes cost $6 each, what is the cost of the hedge?
ANSWERS TO EXERCISES
1. P=56 cm, A=180 sq cm; 2. P=136 m, A=1140 sq
m; 3. P=48 m, A=144 sq m;
4. P=120 ft, A=900 sq ft; 5. P=30 cm, A= 30 sq cm; 6.
P=36 in, A= 54 sq in;
7. P=60 ft, A=173 sq ft; 8. P=36 in, A= 60 sq in; 9. P=18
ft, A= 12 sq ft;
10. P=32 ft, A=48 sq ft; 11. P=32 m, A= 48 sq m; 12.
P=36 ft, A= 60 sq ft;
13. P=62.8 cm, A=314 sq cm; 14. P=31.4 cm, A= 78.5 sq cm;
15. P=18.84 m, A= 28.26 sq m; 16. P=37.68 m, A=113.04 sq m;
17. P=157 m, A= 1962.5 sq m; 18. P=78.5 m, A= 490.63 sq m;
19. 72 cu m; 20. 180 cu ft; 21. 125 cu in; 22. 27,000
cu cm; 23. 1570 cu m;
24. 785 cu m; 25. 125.6 cu m; 26. 196.25 cu m; 27.
4186.67 cc; 28. 65.42 cc;
29.
1046.67 cu in; 30. 314 cu in; 31. 9; 32.
1,000,000; 33. 1,000,000,000;
34. 1728; 35. P=9 ft (108
in), A=2 sq ft (288 sq in); 36. P=14 yd (52 ft), A=12 sq yd (108 sq
ft);
37. P=860 cm (8.6m), A=12000 sq cm (1.2 sq m);
38. P=108 cm (1080 mm), A=200 sq cm (20000 sq mm); 39. 4.5 sq yd
(40.5 sq ft);
40. 600 sq m; 41. 
;
42. 2πy + 6x; 43.
B; 44. A; 45. D; 46. C; 47. A; 48. C;
49. 
(approx 11.5 ft); 50.
10 ft; 51. 216; 52. $511; 53. $695.65; 54.
97.78 cu yd; 55. 20 cu yd;
56. 540 sq ft or 2 gal; 57.
284 sq ft or 1 gal; 58. 181 bushes, $1050.
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