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" # # # %& %U &T &T &V ) * *g *j * * + , - -- -5 .4 .4 .9 0} 0 0 1 2' 2N 4$ 4. 5? 5E 5f 5n 8 8 9 9 9 : : : :  : : : : :! :! :) :) :1 :9 :< :D :G :J :M :Q :S :T #-#-߰&-&H-p n-P --h -*-@--!u-L%k-)g--36-`0i&-3"-6-ߔ# UNIT 8: WORKING WITH SHAPES IN THREE DIMENSIONS EVEN QUESTIONS 2-40 Please refer to this information while working on problems in the packet. (Place SUMMARY information, page 23, here.) 2. The basement of a building is flooded with water to a depth of 18 inches. The basement is rectangular, 48 feet long, and 40 feet wide. Two pumps are being brought in to pump out the water. Each can pump 30 gallons per minute. a. What is the volume of water (in cubic feet) accumulated in the basement? b. How many gallons of water is this? You know that each cubic foot of water is about 7.48 gallons. c. How many hours will it take to completely pump all this water from the basement? (Round to the nearest 0.1 hour.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 4. If the density of an object is less than the density of water, the object will float in water. Conversely, if it is greater, it will sink. Water has a density of about 0.58 ounces per cubic inch. A baseball has a diameter of 2 7/8 and weighs 5 1/4 ounces. a. What is the volume of the baseball in cubic inches? b. How many ounces does each cubic inch of baseball weigh? (This is the density of the baseball.) c. Compare this density to the density of water. Will this baseball float or sink if it falls in water? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 6. If there are about 250 cubic feet in each ton of baled alfalfa, how many tons of baled alfalfa can be stored in a 20 x 40 x 10 rectangular storage area? What are you looking for? What do you need to answer the question? WrHite out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 8. A corn bin is built that is 20 across and 15 high, as shown below. Place bin picture, page 30, here. a. What is the volume of this bin? b. If a bushel of shelled corn is equivalent to 0.8 cubic foot, how many bushels of shelled corn can this bin hold? (Round to the nearest 10 bushels.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 10. The amount of timber on a logging truck is commonly reported in cords, where each cord is 128 cubic feet of wood. The volume of wood is estimated by assuming the trees are shaped approximately like a cylinder. However, the diameter at one end is larger than the diameter at the other end of the log. So a common approximation of the volume is found by using the average of the two diameters to compute the volume. a. The logs on a certain logging truck are all about the same. Each has a diameter of 25 inches at the large end and 14 inches at the small end. Determine the average of the two diameters of these logs. Determine the average of the two diameters of these logs. (Hint: The average is computed by adding up the numbers and dividing by how many numbers youve added.) b. The logs of this truck are 36 feet long. Using the average diameter computed above, compute the volume of each log. (Round to the nearest 0.01 cubic foot.) c. There are 17 logs on this logging truck. What is the total volume of wood on the truck? (Round to the nearest cubic foot.) d. How many cords of wood are on the truck? (Round to the nearest 0.1 cord.) 12. A customer asks, How long will it take to fill this water bed? The water bed reservoir, when filled, is 79 long, 77 wide, and 12 high. You estimate a water- flow rate of about 5 gallons per minute. a. Assuming an essentially rectangular-shaped bed, compute the volume of the filled water bed. b Since each gallon contains 231 cubic inches, how many gallons of water are in the bed? c. Using the flow rate above, about how long will it take to fill the bed? (Round to the nearest minute.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 14. Cans of food products are packed in rectangular-shaped cartons. Suppose a carton is 12 long, 9 wide, and 7 tall. 24 cans, each m easuring 3 3/8 high and 2 7/8 in diameter, are packed in the carton. a. What is the volume of each can? b. What is the volume of the carton? c. What fraction of the cartons volume is not used by the cans? What percentage is this? d. How could this space be better used? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 16. A 15-cubic-foot upright freezer is described as having dimensions of 64 high, 28 wide, and 27 1/4 deep. Compute the volume of the freezer from the measurements given, and compare it to the advertised volume. Do t*he values agree? Why not? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 18. As manager of a pet store specializing in aquariums and aquarium supplies, you often build custom aquariums. A customer has asked you to design a tall tank that is to fit in a small corner. The inside dimensions of the completed tank, shown to the right, are 36 3/4 tall and 10 inches wide on the back sides. (The back corner is a 90o angle.) Place tank picture, page 33, here. a. If two of these tanks were placed side by side, with the front faces touching, what geometric figure would be represented? b. Compute the volume of the geometric figure represented by two of the tanks. What then would be the volume of just one of the tanks? c. Since a gallon contains 231 cubic inches, how many gallons of water will the tank hold? (Round to the nearest gallon.) 20. A patient arriving at the hospital reports drinking a thermos of coffee on the way to the hospital. You must record this intake of fluids, but the patient doesnt know how much the thermos contained. After a brief discussion, you figure that the inside flask must have been about 7 tall and had a diameter of about 3. a. Identify the approximate geometric shape of the inside flask of a thermos container, and compute the volume for this patients thermos. b. If each cubic inch is equivalent to about 16.4 cubic centimeters, about how much coffee did the patient drink? (Round to the nearest 100 cc.) What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 22. An unmarked flask is found, as shown below. You estimate that it is about 8 cm across at the base, and about 12 cm deep (up to the neck). What shape can you use to approximate the shape of the flask? What is the approximate volume of the flask? (Round your answer in cubic centimeters to the nearest 50 cc.) Place flask picture, page 35, here. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 24. The inside of a home bathtub typically measures approximately 50 long and 20 wide. Suppose that for bathing, you fill it about 8 deep. a. Assuming a rectangular shape of the tub, what is the volume of the bathtub water? b. If each gallon is 231 cubic inches, how many gallons of water is this? c. Suppose, if showering, you would use about 2 gallons per minute for a 10- minute shower. Which would use more water, showering or taking a bath? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 26. The restaurant kitchen has several sizes of unmarked ladles used to provide uniform servings. You know that each fluid ounce is about 1.80 cubic inches. You measure the size of each ladle, as shown in the illustration. What is the level capacity of each ladle shown below? (Round to the nearest 0.5 ounce.) Place ladle picture, page 36, here. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 28. A common guideline for air exchange in a school classroom is for the air conditioning to supply about 1600 cubic feet of air per occupant every hour. Suppose a classroom is designed to hold 20 occupants (students). The room is rectangular, 20 feet across the front, 40 feet from front to back, and the walls are 10 feet high. a. How much air should be supplied each hour for 20 students in the classroom? b. What is the volume of air in the classroom? (Actually the volume of the occupants should be deducted from this volume. Ignore this for the exercise.) c. How many times each hour should the air volume in the classroom be replenished by the air conditioning? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 30. A pile of sand dumped by a hopper is cone-shaped. The top of the pile is 8 1/2 above ground level. The diameter of the base is 18 1/4 wide. Convert the measurements to yards and determine how many cubic yards of sand are in the pile. What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 32. A Quonset hut is being built, as shown below. You are going to insulate the ceiling using rolls of insulation. How many square feet of insulation will you need to completely cover the inner surface of the roof? Place Quonset hut picture, page 38, here. 6 What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 34. A 90 straight concrete sidewalk is to be constructed. It will be 3 wide and 4 deep. a. Since concrete is normally ordered in yards (that is, cubic yards), convert the measurements from inches and feet to yards. b. Identify the geometric figure in the construction that you can use to compute its volume. Compute the total volume of the construction, in cubic yards. (A sketch might be helpful.) c. Allow 10% for spillage. How many cubic yards should you add to your needs for spillage? What will &your total needs be, rounded up to the nearest cubic yard? What are you looking for? What do you need to answer the question? Write out the methods that you will use to solve the problem and show your work in calculating the answer(s). Your answer(s) are (make sure the units used are correct): 36. The figure below shows the dimensions of a T-shaped layout that must be excavated to a depth of nine feet. Place diagram, page 40, here. a. Identify geometric figures in the construction that you can use to compute its volume. Compute the total volume of soil to be excavated. b. Material removed from an excavation occupies about 25% more volume than when it was in place. What will be the volume of the loose material to be" hauled away? c. If each dump-truck bed can hold 12 cubic yards, how many truck loads of excavated material will there be? 38. Baghouses are used in filtering exhaust air from coal-fired power plants. A certain baghouse contains 100 cylindrically shaped filter bags, as shown below. Each bag is 33 feet tall and has a diameter of 1 foot. The side and top surfaces are used for filtering. Place diagram, page 41, here. a. Compute the surface area of one of the filter bags. b. What is the total filtering surface area of the baghouse? c. Someone suggests that it would require less maintenance to use twenty-five 2-foot-diameter bags in the baghouse, instead of the 100 smaller bags. Compute the total filtering surface area for the proposed arrangement. Would the filtering surface area be better (more area), the same, or worse (less area)? 40. The weight of a flat steel plate is being finely adjusted. The plate is presently 1.00 thick, 20 long, and 4 wide, and weighs 22.50 pounds. You plan to drill several 1/2-diameter holes through the plate to bring its weight to within 0.05 pound of the desired weight of 22.00 pounds. a. What is the volume of metal presently in the plate? b. What does each cubic inch of the steel plate weigh (what is its density)? c. What would be the volume of metal removed by drilling one hole? What would be the weight of metal removed from this hole? (Hint: Use the weight per cubic inch calculated above.) d. How many holes should you drill? DSET|(H->"9 *6*>"9DSET(H-9>96*=9DSETR -t-(--   -TUnit 8 Even Questions