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Math 112 – Test #3 Review Name: ___________________ Please show your work on all problems, and draw figures where appropriate. 1. What is the volume of a conical-shaped volcano that has a circular base of 35 meters across and a height of 25 meters? 2. Knowing that one meter is 3.28 ft, and that one gallon of water weighs ~8 pounds, and that one kilogram equals ~2.2 pounds, then how many kilos does a cubic meter of water weigh? [Remember that there are ~7.5 gallons per cubic foot.] 3. Using a scale of ¼ inch = 1 foot, a model railroader built a cardboard model of a bridge. How much would the actual steel bridge have weighed if her cardboard model weighed 6 ounces and steel is 11 times heavier than the same amount of cardboard? [Remember that 1 pound = 16 ounces.] 4. Joshua buys a cylindrical tank for storing water that is 4.5 feet high and 6 feet across. What is the best answer for the volume of his tank? Explain. a) about 125 cu ft b) 127.2345 cu ft c) about 80 cu ft d) about 40 cu ft 5. A house has a floor area of 1650 square feet. What is the area of the house in square meters? [3.28 ft = 1 m .] 6. How much mulch will you need to cover a rectangular 30’ by 45’ garden with a 4inch layer of mulch? If the mulch is sold by the cubic yard, how many cubic yards would you need to buy? 7. A cardboard box with a top, a bottom, and four sides is W feet wide, L feet long, and H feet tall. Find a formula for the surface area of this box in terms of W, L, and H. Explain why your formula is valid for any box. 8. A rectangle contains 91 1-sq-cm squares. What is the area of the parallelogram formed by cutting a 21-sq-cm triangle off one end and pasting it to the opposite end? Draw the figure and explain your answer. 9. Mark and Susan stand 12 feet apart and hold a measuring tape between themselves. Mark holds the zero end of the tape on the ground at his feet, and Susan holds her end of the tape 4’ 6” above the ground at eye level. What measure, in feet and inches, should Susan see on her end of the tape? 10. Draw a figure that illustrates the multiplication of 4 12 5 34 . Use your figure to calculate 4 12 5 34 without using a calculator. 11. Calculate the median and the upper and lower quartiles for these scores. 73, 82, 64, 67, 59, 63, 44, 73, 44, 50, 74, 95, 58, 70, 77, 66, 59, 57, 67, 62, 59, 62, 82, 50, 72, 43, 76, 42, 58, 56, 38, 59, 46, 82, 75, 73, 67, 83, 67, 78, 73, 82, 50, 93, 61, 56, 42, 64, 84, 44, 55, 58, 28. Then construct a box and whisker plot for the data. Back Page Ideas 1. A 1-liter container has marks on the side (0.1, 0.2, 0.3, etc, with ten little marks between each of those that represent hundredths). [So, for example, a water level up to the third little mark above 0.2 would be 0.23 liters.] a) If the beginning water level was 0.42, and the level after you submerged a copper bracelet was 0.61, what is the volume of the bracelet in cubic centimeters? [Remember that 1 liter contains 1000 cm 3 ] b) What is the value of the bracelet, if a cubic centimeter of copper weighs 8.94 grams and copper is worth $0.004 per gram? 2. A cone without a base is made from a large quarter-circle. The base of the cone is a smaller circle whose circumference is 10π inches. What is the surface area of the cone? 3. Carefully draw a figure whose linear measurements are exactly twice as long as the measurements of this figure. Use the dot to help. . ╣ Brief answers: 1. ~ 8000m3 ; 2. ~ 960kg / m3 ; 3. ~455,000 lbs; 4. B; 5. ~ 150m 2 ; 6. 25 16 23 yd 3 ; 7. A = 2LW + 2HL + 2HW; 8. 91cm 2 ; 9. ~12’ 9 12' 9 32 " , 10. 25 78 "