7BOBO-dHHHHHH-HH--pC9 - -Z`AxHH(FG(HH(d'@-$*-lA/UF@-@-d- , *x*`-DF-$9v -@!(}DSET<=</]---,y-t-vy-(-vy-d-vy--v y-p-v y-$-vy-P-vy-,-vJy- -vpy- -vy-H-x!my-x-v$zy-<-v'9y-4-v)y--v,~y--v.y--v2y--v5y-l-v7y--v:y-|x34OP^_ )*+TUV     ab9:;;<=     | } ~  R S T U    " # $ M N O    456%&';<=WXY56789:;<=>?@ABCDEFGHIJefghopqrs()*+,-./0klmnop    ,-./XYZ wxyz{|} !i!j!k!l!m#j#k#l#m#n#o#p#q#r#######$($)$*$+$,$-$.$/$0$1$2$m$n$o$s$t$u$v$w$x$y$z%>%?%%%%&/&0&1&2&3&4&5&6&P&Q&R&S&|&}&~&&&&&&&&&&&'1'2'3'4'5'6'7'8'9''( ( ( ( (((((((((((((()))o)p)q)r)s)t)u)v)w)x)y))))))))*&*'****+t+u+v+w+x+y+z+{+|+}+++++++,3,4,5,6,7,8,9,:,;,<,=,x,y,z,|,},~----------------.....-.../................../e/f090:0;0<0=0>0?0@0011111111 1!1"1#1L1M1N11111111111222222222222222223K3L3M3N3O4 444444,4-4.4W4X444444456 6 66666;6<6=6>6?6@6A6B6h6i6j6k6l6m6n66666677777777777778888888889999999G9H9I99999999999999::::::::;B;C;D;E;F;G;n;o;p;q;s;u;v;<<<<<<<<<<< O P                        u x     = J   % h k s p       } > E !g !i #r $o $v $w $z $ $ $ $ $ $ % % %# %& %3 %6 &6 '3 ' ' ' ' ( ) +J +M +} ,z - . 1 2 4  5 5A 5D 5] 5` 7 7 7 7 9 9  -8 -"-- }-e;-$-,---`"M-&M-*-.-,2-6-9- UNIT 8: WORKING WITH SHAPES IN THREE DIMENSIONS ODD QUESTIONS 1 - 39 Please refer to this information while working on this packet. (Place Summary information, page 23, here.) 1. A round childrens pool measures 60 diameter, and is 12 deep when filled. Assume that the sides are vertical. a. Compute the volume of the pool. b. Using the fact that each gallon of water occupies 231 cubic inches, how many gallons of water are used to fill this pool? 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): 3. When a hurricane or other disaster is expected, it is often wise to secure a fresh- water reserve . One method often used is to clean and fill the home bathtubs. Suppose your bathtub interior measures approximately 54 long and 22 wide, and it can be filled to a depth of 11 inches before reaching the overflow drain. a. Assume a rectangular shape. What volume of water (in cubic inches) can this tub contain? b. If each gallon occupies a volume of 231 cubic inches, how many gallons of water can the tub hold? c. If you and your family could live on 3 gallons a day in an emergency situation, about how many days would your water reserve last? (Assume no loss to evaporation.) 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): 5. Consider the shape of a hot-air balloon, as illustrated below. Suppose that the air conditions are such that each cubic foot of heated air within the balloon is able to lift 0.020 pounds of payload. Place balloon picture, page 28, here. a. Identify the geometric figures that could be used to approximate the shape of the hot-air balloon shown. Compute the volume of hot air inside the balloon in cubic feet, using the dimensions shown in the illustration. (Round to the nearest cubic foot.) b. Using the amount of lift available from each cubic foot of hot air given, compute the total weight that could be lifted by this balloon. (Round to the nearest pound.) 7. A circular stock tank is dug, as shown below. After a good rainfall the tank fills to an average depth of about 4 and measures 80 across. Place stock tank drawing, page 29, here. a. Identify the geometric figure that can be used to approximate the shape of the tank. Compute an estimate for the volume of water in the tank. b. If each cubic foot of water is equivalent to 7.48 gallons, about how many gallons of water have accumulated in the tank? (Round to the nearest 100 gallons.) 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): 9. Suppose that an area receives 12 of rainfall during a season. This means the amount of rain is equivalent to water that is 12 deep over the entire area. a. How many cubic feet of rain have fallen on one acre of land that has an area of 43,560 square feet? b. Each cubic foot is equivalent to about 7.48 gallons. If you had to provide irrigation water of the same amount, how many gallons of water would you have to pump? (Round to the nearest gallon.) 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): 11. The cylindrical columns in the shopping mall need to be repainted. Each of the 28 columns is 14 feet tall ;and measures 56 1/2 around. The paint youve chosen is advertised to cover 400 square feet per gallon. a. Compute the surface area of each column, and the total surface area of all the columns to be painted. (Round the final answer to the nearest square foot.) b. How many gallons of paint will be needed? (Round up to the nearest gallon.) 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): 13. A hotel is refurbishing the lampshades in 50 of their rooms by covering the outside of each lampshade with new material. The lampshades are cylindrically shaped, 12 diameter and 16 tall. Each room has two of these lampshades. Approximately how many square yards of fabric will be needed to complete the job? (Ignore waste.) 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): 15. You are packaging an order of candy for a customer. The candy comes in boxes that are 4 x 4 x 4 cubes. The largest carton your company uses is 4 x 2 x 2. a. Convert the dimensions of the carton to inches. What is the volume of the carton, in cubic inches? b. What is the volume of each candy box? c. How many volumes of candy boxes can fit into the volume of the carton? d. Why might using a method like this not always work? (Hint: Suppose you were packaging boxes that measure 4 x 4 x 3 1/2.) 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): 17. Employees suggest that the water cooler be supplied with 4-oz paper cups rather than the paper cone cups supplied by the water company. They say that the cone-shaped cups dont hold enough water. Use the sketch below to determine if the cone-shaped cups hold more or less water than a 4-oz paper cup. (Each cubic inch is the same as 0.554 oz.) Place cone drawing, page 32, 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): 19. A telescoping aerial lift (better known as a cherry-picker) is designed to be able to reach from 13 feet out to 21 feet. It can reach all the way around a 360o hemisphere, except for a small vertical section, as shown below. As part of an advertising brochure, you need to compute the cubic feet of air space that the lift is able to service. Place lift diagram, page 33, here. a. Identify the geometric figures in the construction that you can use to compute the volume. Compute the total volume that the lift could service, if it could service all the space within its farthest reach, even inside the 13 minimum. b. Compute the volume of the space not able to be reached due to the minimum reach of 13. Determine the amount of air space that the lift can reach, adjusted for the air space that the lift cant reach due to the minimum extension distance. (This wont yet take into account the vertical volume that cant be reached. c. Use a similar method to determine how much additional air space to deduct, due to the vertical volume that cant be reached. (Hint: Above you calculated the total air space and adjusted for the amount that couldnt be reached due to the minimum extension. Here you need to calculate the additional amount that cant be reached and adjust for the volume that has already been corrected for above. Make a sketch!) d. What can you report as the total volume of air space that is serviceable by the lift? (Round to the nearest cubic foot.) 21. Your body volume can be approximated at home in your own bathtub as follows. Fill the bathtub to the overflow drain. Submerge yourself in the tub. Allow time for the displaced water to drain and the water level to return to the level of the overflow drain. Get out of the tub and measure the drop in water level (the distance below the overflow drain). Suppose such a procedure in a 50 x 20 rectangular bathtub results in a drop in the water level of 2. What is your body volume? 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): 23. A cake recipe calls for a cake pan measuring 113/4 long, 71/2 wide, and 1 3/4 deep. But you only have a slightly larger pan that measures 131/2 long, 83/4 wide, and 13/4 deep. a. Compute the volume of each cake pan, if it were filled to the top with cake. b. Suppose that the cake fills the smaller pan when cooked. In the larger pan, would you expect the same cake to be more or less that 1 thick? 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): 25. A cylindrically shaped, 1-pound coffee can is frequently used for storing miscellaneous items and liquids. Such a can has an inside diameter 37/8 and is 51/4. a. Compute the volume of the can. b. A liquid quart is 57.75 cubic inches. Would a filled 1-pound coffee can make a good approximation of a quart? How much more or less than a quart is it? 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): 27. You have three round tomatoes, each about 3 diameter, that you can process to make stewed tomatoes. a. Identify the figure that roughly corresponds to the shape of a tomato. What is the total volume of the three tomatoes? b. Is this more or less than the volume of stewed tomatoes that you could get from a filled 1-pound can that measures about 3 inside diameter and 41/2 tall? How much more or less? 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): 29. An engine has been adjusted to change the piston stroke. Each piston now has a stroke of 4.031 (see figure below). Each piston has a diameter of 3.125. On this eight-cylinder car, what would be the new total volume displacement (of all the pistons)? (Round to the nearest cubic inch.) Place picture, page 37, 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): 31. A natural gas company runs an 8 pipeline (8 inside diameter) to a new subdivision of houses that is 10 miles away. a. Identify the geometric figure represented by the pipeline. At the transmission pressure, how many cubic feet of natural gas are stored in the pipeline? (Round to the nearest 100 cubic feet.) b. The reduction in pressure at the customers meter results in about 7 times more volume. How many cubic feet of gas stored in the pipeline are available to the customer? 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): 33. Suppose the grab bucket shown below is used to load gravel into dump trucks. The dimensions on the drawing can be used to estimate the capacity of the bucket. Place bucket drawing, page 38, here. a. Identify the geometric figure that can be used to estimate the volume of the grab bucket. b. Using the dimensions in the figure, calculate what volume of gravel the bucket should be able to hold. (Assume that the gravel will be level with the top of the bucket. 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): 35. A double-acting cylinder has a 4-diameter barrel, a 13/4-diameter rod and a 241/2 stroke. When the cylinder is retracted, as shown below, the amount of hydraulic fluid in the barrel is the volume of the barrel less the volume occupied by the rod. Place cylinder drawing, page 39, here. a. Compute the volume of the barrel. b. Compute the volume of the rod (the portion within the barrel). c. Compute the amount of fluid needed to fill the barrel when the rod is retracted, as shown. Convert this amount to gallons of hydraulic fluid. You know that each gallon of fluid occupies 231 cubic inches. 37. After completing a concrete pour, you have about 0.4 cubic yard of concrete remaining. You would like to use the excess to make curcular patio stones. You have a ready source of forms to make 18-diameter stones. If you make each patio stone 3 thick, how many patio stones can you obtain from the leftover concrete? 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): 39. A solid concrete stoop and steps, as shown below, are to be constructed on top of an existing foundation. As shown, the landing (or upper step) is to measure 3 square, and each of the two lower steps will measure 3 x 1, rising 8 for each step. You need to determine how much concrete will be needed. Place step drawing, page 41, here. a. Since concrete is normally ordered in yards (that is, cubic yards), convert the measurements from inches or feet to yards. b. Identify geometric figures in the construction that you can use to compute its volume. Compute the total volume of the construction, in cubic yards. DSET|(H->"9 *6*>"9DSET(H-9>96*=9DSETR -h-\--   -DUnit 8 Odd Questions