# Lesson Perimeter, Area, and Volume by Rapalje

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About rapaljer: Retired Professor of Mathematics from Seminole State College of Florida after 36 years.

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 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.

 Dr. Robert J. Rapalje Altamonte Springs Campus Contact me at: Phone number:  NONE Retired!! OFFICE:          NONE Copyright © Seminole State College of Florida, 1997

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