MATH 3162 Pre-Test Unit 3 Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the surface area of the solid. 1) 1) Right triangular prism with a height of 12 cm and its base is an equilateral triangle with sides of length 8 cm. Round your answer to the nearest hundredth. A) 343.43 cm2 B) 439.43 cm2 C) 315.71 cm2 D) 406.63 cm2 2) 2) a = 3 ft, b = 4 ft, c = 3 ft Rectangular prism A) 33 ft2 B) 72 ft2 C) 54 ft2 D) 66 ft2 3) 3) Right circular cone with r = 6 cm, h = 5 cm A) 113.0 cm2 B) 94.2 cm2 C) 78.5 cm2 D) 260.2 cm2 4) 4) Right square pyramid with a side of 8 in. and a slant height (height of the triangular face) of 7 in. A) 176 in.2 B) 128 in. 2 C) 120 in. 2 D) 72 in.2 1 Solve the problem. 5) 5) 50 m 100 m 4 lanes are added around the outside of the track shown above. Each lane is 1 meter wide and the lanes are immediately next to each other with no space in between. If Teresa runs once around the outside lane, and Martina runs once around the inside lane, how much further does Teresa run than Martina? A) 3π m B) (50 + 6π ) m C) 6π m D) 4π m 6) Which is the best deal? A: Six small grapefruits for a dollar. B: Four medium size grapefruits for a dollar C: Three large grapefruits for a dollar 6) Assume that all the grapefruits are spherical, that the small grapefruits have a diameter of 3 inches, the medium grapefruits have a diameter of 3.5 inches, and the large grapefruits have a diameter of 4 inches. A) C B) A and C C) B D) A 7) What is the ratio of the surface areas for a pair of similar cylinders when the ratio of the heights is 1: 3? A) 1:3 B) 1:9 C) 1:27 D) Not enough information given 7) 8) If a pizza of diameter 6" will feed one, how many will a pizza of diameter 18" feed? Assume that both pizzas have the same thickness. A) 27 B) 4 C) 9 D) 3 8) 2 9) Frustum of a cone 9) r 2r A small cone has been removed from the top of the original cone. What is the ratio of the volume of the original cone to the volume of the small cone which was removed, given that the radius of the original cone is twice the radius of the small cone? [Hint: Use similar triangles] A) 8 : 3 B) 2 : 1 C) 4 : 1 D) 8 : 1 10) If the height of a right circular cylinder is quadrupled and the radius is divided by three, how is the volume changed? 4 16 A) It is multiplied by B) It is multiplied by 3 9 C) It is multiplied by 4 9 D) It is multiplied by 9 4 11) The areas of the faces of a rectangular box are 48 m 2 , 96 m 2 , and 288 m 2. A second box is cubical and each of its faces has area 16 m 2 . Find the ratio of the volume of the first box to the volume of the second box. A) 16 : 1 B) 12 : 1 C) 18 : 1 10) 11) D) 324 : 1 12) Find the volume. 12) 12 m 4m Cone with hemispherical top A) 1507.2 m 3 B) 602.88 m 3 C) 137.04 m 3 3 D) 1055.04 m 3 13) Find the volume. Round to the nearest whole number, if necessary. 13) 11 ft 62 ft Cylindrical grain silo with hemispherical top A) 220,392 ft3 B) 8181 ft3 C) 95,604 ft3 D) 64,407 ft3 14) Find the surface area. Round to the nearest whole number, if necessary. 14) 71 ft 62 ft Cylindrical grain silo with hemispherical top A) 19,867 ft2 B) 16,848 ft2 C) 25,906 ft2 D) 276,748 ft2 15) Two corresponding sides of similar polygons are in the ratio of 8:7. If the area of the smaller figure is 512 square meters, what is the area of the larger figure? A) 3584 m B) 134,217,728 m C) 392 m D) Not enough information given 15) 16) A room measures 15 ft by 19 ft. The ceiling is 10 ft above the floor. The door is 3 ft by 7 ft. A gallon of paint will cover 78.2 ft2. How many gallons of paint are needed to paint the room (including the 16) ceiling and not including the door). Round your answer up to the next whole number. A) 9 gal B) 13 gal C) 4 gal D) 21 gal 17) A small can of juice contains 16 fl oz. A large can has twice the base circumference of the first. How much juice is in the large can if both cans are right circular cylinders and the second can is similar to the first? A) 128 fl oz B) 64 fl oz C) 256 fl oz D) 32 fl oz 17) 18) Juice comes in cylindrical cans of two sizes. The second can has twice the diameter of the first and is half as tall. Find the ratio of the amount of juice in the second can to the amount of juice in the first can. A) 2 : 1 B) 1 : 2 C) 1 : 1 D) 4 : 1 18) 4 19) Paul's Pizza Pipers sell personal 6-inch pizzas. The dimension given is the diameter of the pizzas. Below is a partial sample of their menu. Deluxe Sausage Mushroom Cheese 19) $9.99 $5.99 $5.50 $4.99 Taking into account that $0.70 is charged on each additional topping, is it a better deal to buy the deluxe pizza or to buy a cheese pizza with 2 additional toppings? What is the price per square inch of the better deal? A) Deluxe pizza; $0.09 B) Deluxe pizza; $0.35 C) Cheese pizza; $0.23 D) Cheese pizza; $0.20 Choose the most reasonable unit of measure. 20) Can of food: 422 A) 4220 g B) 422 g 21) Soup can volume 333 20) C) 0.0422 g (mL, L) 21) A) mL B) L 22) One strand of hair: A) 20 mg 22) B) 12 mg 23) Basketball court length 24 A) km 24) A baseball: A) 0.146 g 25) Hammer length 37 A) km 26) Five liters of water: A) 50 kg 27) Horse weight 460 A) mg D) 0.422 g C) 200 mg D) 2 mg B) m C) cm D) mm B) 0.0146 g C) 1460 g D) 146 g (mm, cm, m, km) 23) 24) (mm, cm, m, km) 25) B) mm C) cm D) m B) 500 kg C) 15 kg D) 5 kg 26) (mg, g, kg) 27) B) g C) kg Solve the problem. Use 3.14 as an approximation for π where appropriate. 28) The Great Pyramid of Giza was built around the year 2560 BC. It was originally 481 ft high with a square base measuring 751 ft on each side. Its slant height was 611 ft. Find the lateral surface area of the Great Pyramid. Round your answer to four significant digits. A) 917,700 ft2 B) 722,500 ft2 C) 90,430,000 ft 2 D) 1,481,700 ft2 1 29) At $2.70 per ft3 , how much will it cost to fill an ice chest with dimensions of 8 ft x 7 ft x 12 ft? 2 A) $1215.00 B) $2073.60 C) $1944.00 5 D) $2916.00 28) 29) 30) A cylindrical drain pipe is 7 inches across the top and about 12 inches high. How many cubic inches of water could it hold (to the nearest hundredth)? A) 461.58 in.3 B) 1846.32 in.3 C) 923.16 in. 3 D) 527.52 in. 3 30) 31) How many square centimeters of glass does it take to make the bottom and sides of a cubic shaped aquarium with an edge of 40 cm? A) 6400 cm2 B) 9600 cm2 C) 64,000 cm2 D) 8000 cm2 31) 32) A certain marine engine has cylinders that are 3.35 inches in diameter and 5.13 inches deep. Find the total volume of 8 cylinders (to the nearest hundredth). A) 723.10 inches3 B) 45.19 inches3 C) 361.55 inches3 D) 863.40 inches3 32) 33) An aluminum cylindrical juice can has a height of 4 in. and a radius of 6 in. How many square inches of aluminum are needed to make the can? A) 376.8 in.2 B) 188.4 in.2 C) 452.2 in.2 D) 301.4 in.2 33) Find the circumference of the circle. Use 3.14 for π. 34) 34) 14 cm A) 62.17 cm B) 43.96 cm C) 307.72 cm D) 31.08 cm 35) 35) 6 cm A) 18.84 cm B) 26.64 cm C) 56.52 cm D) 13.32 cm 36) Use the formula for the circumference of a circle to find the arc length s. 36) 7 in. A) 14.66 in. B) 401.07 in. C) 0.15 in. 6 D) 7.33 in. 37) 14 yd 37) A) 153.86 yd 38) B) 43.96 yd C) 21.98 yd D) 87.92 yd 15 yd 38) A) 94.20 yd B) 23.55 yd C) 47.10 yd D) 176.63 yd 39) 39) 11 yd. A) 379.940 yd. B) 13.970 yd. C) 34.540 yd. D) 69.08 yd. 40) 40) 14 in A) 43.96 in B) 87.92 in C) 153.86 in D) 21.98 in 41) Use the formula for the circumference of a circle to find the arc length s. 41) 19 in. A) 0.06 in. B) 39.79 in. C) 19.9 in. 7 D) 1088.62 in. Find the perimeter. 42) 42) 156 ft A) 24,336 ft B) 936 ft C) 780 ft D) 795 ft 43) 43) 23 m 23 m 8m A) 52 m B) 54 m C) 92 m D) 46 m 44) 44) 38 m 33 m A) 71 m B) 104 m C) 142 m D) 109 m 45) 45) 29 m 12 m 12 m 23 m A) 276 m B) 29 m C) 41 m D) 76 m Solve the problem. Round your answer to the nearest hundredth if necessary. 46) In a certain coastal basin, the sea water contains 3.5 grams of salt per 1000 milliliters of water. How many grams of salt would be in 2 liters of the sea water. A) 7 grams B) 0.07 grams C) 70 grams D) 700 grams 46) 47) A 2500 g bag of sugar was on sale for $0.95. How much would you have to pay for 30 kg of sugar? A) $12.63 B) $11.40 C) $114.00 D) $1140 47) 48) Maha checked the outside temperature at noon one day and found it was 26° C. At 10 PM when he checked, the outside temperature was 20° C. How much, in degrees Fahrenheit, did the temperature drop between noon and 10 PM? A) -10.8°F B) 3.33°F C) -21.2°F D) 10.8°F 48) 8 49) One-half serving of soy sauce contains 389 milligrams of sodium. How many grams of sodium from soy sauce are included in an egg-foo-young dish made from 4 servings of soy sauce? Round results to the nearest tenth of a gram. A) 155.6 g B) 0.1 g C) 3.1 g D) 97.2 g Complete the following. Round to the nearest tenth. 50) 46 kg = lb A) 48.8 51) 15 L = 50) B) 116.8 C) 101.2 D) 20.7 qt A) 18.0 52) 4 lb = 51) B) 14.2 C) 6.8 D) 15.8 g 52) A) 1860.0 53) 22 km = 49) B) 908.0 C) 1792.0 D) 1680.0 mi A) 20.8 53) B) 35.4 C) 23.3 D) 35.2 Find the area indicated. Use 3.14 as an approximation for π. 54) 54) 6 cm Find the area of the circle that circumscribes the square. A) 56.52 cm2 B) 36 cm2 C) 113.04 cm2 55) D) 26.64 cm2 15 yd 55) Find the area of the inscribed circle. A) 47.1 yd2 B) 94.2 yd2 C) 706.5 yd2 D) 176.625 yd2 56) 56) 6.5 in. Find the area of the circle. A) 81.64 in. 2 B) 40.82 in. 2 C) 530.66 in. 2 9 D) 132.665 in. 2 57) 57) a = 11 in. Find the area of the portion of a circle given that a circle has 360° and the portion has 270°. Round your answer to the nearest tenth. A) 506.6 in. 2 B) 285.0 in. 2 C) 51.8 in. 2 D) 71.2 in. 2 Find the area of the polygon. 58) 58) 5 in. 10 in. A) 25 in. 2 B) 15 in. 2 C) 50 in. 2 D) 100 in. 2 59) 59) 3 cm A) 4.5 cm2 B) 9 cm2 C) 18 cm2 D) 6 cm2 60) 60) 49 in. 55 in. 24 in. A) 1200.5 in.2 B) 588 in. 2 C) 1347.5 in. 2 D) 1176 in. 2 61) 61) 16 cm A) 64 cm2 B) 512 cm2 C) 256 cm2 10 D) 251 cm Find the volume. 62) 62) 9.2 cm 6.6 cm 4.1 cm Rectangular prism A) 64.82 cm3 B) 248.952 cm3 D) 248.952 cm2 C) 19.9 cm3 63) 63) 5m 16 m Right circular cylinder Use 3.14 for π. A) 251.2 m 3 B) 5024 m 3 C) 502.4 m 3 D) 1256 m 3 64) 64) Radius is 2.0 in.. Use 3.14 for π. Round your answer to the nearest thousandth. A) 33.493 in.3 B) 267.947 in.3 C) 16.747 in. 3 D) 18.84 in.3 11 65) 65) 51 m 28 m Circular cone Use 3.14 for π. Round your answer to the nearest whole number. A) 76,227 m 3 B) 125,550 m 3 C) 41,850 m 3 Convert the units. 66) 3 cups = fluid ounces A) 6 67) 591 mm = 68) 18 yards = C) 48 D) 12 B) 59,100 cm C) 59.1 cm D) 5.9 cm 67) feet 68) A) 162 B) 54 69) 480 seconds = C) 648 69) B) 20 70) 76 quarts = D) 216 minutes A) 8 C) 15 D) 4 gallons A) 304 70) B) 19 C) 152 D) 38 mL 71) A) 2.1 mL B) 2100 mL 72) 12,000 pounds = A) 5 73) 59 km = 66) B) 24 cm A) 5910 cm 71) 21 L = D) 1495 m 3 C) 21,000 mL D) 0.021 mL tons 72) 1 2 B) 7 C) 6 D) 6 B) 0.059 m C) 0.59 m D) 5900 m m A) 59,000 m 73) 12 74) 11 kg = mg 74) A) 0.011 mg 75) 15 yd2 = B) 11,000,000 mg C) 0.11 mg D) 1100 mg ft2 75) A) 45 B) 405 76) 637 g = C) 180 D) 135 mg 76) A) 63,700 mg 77) 48 inches = B) 0.637 mg C) 0.0637 mg D) 637,000 mg feet 77) A) 16 B) 4 78) 1728 in.2 = C) 0.33 D) 144 ft2 78) A) 13 B) 192 C) 11 D) 12 Find the area of the figure. 79) 83 m 83 m 79) 83 m 62.25 m 83 m 83 m 83 m A) 228.25 m 2 B) 18,944.75 m 2 C) 12,055.75 m 2 D) 13,778 m 2 80) 80) 15 in. 30 in. 10 in. 7 in. A) 480 in.2 B) 370 in. 2 C) 260 in. 2 D) 220 in. 2 81) Each square is 7 ft by 7 ft. A) 245 ft2 81) B) 294 ft2 C) 588 ft2 13 D) 392 ft2 82) 82) 10.5 m 5.6 m 7m 3.5 m 14 m A) 24.5 m 2 B) 171.5 m 2 C) 12.25 m 2 Select the best answer. 83) The outside temperature on a warm summer day might be about A) 27°C B) 81°C C) 13.5°C 84) An average woman's height might be A) 2.7 m B) 15 m D) 85.75 m 2 83) D) 40.5°C 84) C) 0.5 m D) 1.5 m 85) You might go ice skating if the outside temperature is about A) -1°C B) -41°C C) 11°C D) 21°C 86) The area of an average-sized bedroom might be about A) 13 m 2 B) 2.1 m 2 C) 91 m 2 Make the following conversions to the nearest degree. 87) 33°C = °F A) 1°F B) 50°F 85) 86) D) 100 m 2 87) C) 117°F D) 91°F 88) 88°F = °C A) 190°C B) 126°C C) 31°C D) 17°C 89) 0°C = °F A) 52°F B) 100°F C) 0°F D) 32°F 90) -31°C = A) -17°F 88) 89) °F 90) B) -24°F C) -56°F D) 35°F Provide an appropriate response. 91) Which would take longer, a person running a 15 K (kilometer) race or running a 15-mile race (assuming he/she runs at the same rate of speed)? Explain your reasoning. A) The 15 K race would take longer since 15 kilometers is longer than 15 miles. B) The 15-mile race would take longer since 15 miles is longer than 15 kilometers. 92) Which would be the better buy, a gallon of milk for $3.25 or a 3-liter container of milk for $3? Explain your reasoning. A) The 3-liter container is the better buy. There is more liquid in 3 liters than in one gallon. B) The gallon is the better buy. There is more liquid in one gallon than in 3 liters. 14 91) 92) 93) A hybrid car manufacturer made a vehicle that the company claimed got 29 kilometers per liter. What would be the approximate equivalent gas consumption in miles per gallon? A) About 5 miles per gallon B) About 69 miles per gallon C) About 141 miles per gallon D) About 59 miles per gallon 93) 94) If a person were driving 162 kilometers per hour on a U.S. highway with a speed limit of 70 miles per hour, would he likely be speeding? A) Yes, 162 kilometers per hour is about 100 miles per hour. B) No, 162 kilometers per hour is about 65 miles per hour. 94) Indicate the metric unit that would be best used to express the mass of the object. 95) A flower petal A) grams B) kilograms C) milligrams 96) A car key A) milligrams B) grams C) kilograms 97) A living room sofa A) kilograms B) milligrams C) grams 95) 96) 97) Solve the problem. Use 3.14 for π. Round to the nearest tenth, if necessary. 98) The width of a piece of paper is 8.5 in., the length is 11 in., and the thickness is 0.0043 in. There are 3000 sheets sitting in a cabinet by the copy machine. What is the volume occupied by the paper? A) 1206.2 in.3 B) 1935.0 in. 3 C) 12.1 in. 3 D) 251.6 in.3 99) A cylindrical drain pipe is 6 in. across the top and about 12 in. high. How many cubic inches of water could it hold? A) 1356.5 in.3 B) 339.1 in. 3 C) 678.2 in. 3 D) 452.2 in.3 100) A spherical dog toy has a radius of 5.4 cm. Find the volume. A) 659.2 cm3 B) 5274.0 cm3 C) 91.6 cm3 15 98) 99) 100) D) 82.4 cm3 Answer Key Testname: 3162-UNIT-3-PRE-TEST 1) A 21) A Objective: (12.3) Find the Surface Area of a Solid Objective: (12.1) Choose Appropriate Metric Measurement 2) D 22) D Objective: (12.3) Find the Surface Area of a Solid Objective: (12.1) Estimate the Mass of Object 3) D 23) B Objective: (12.3) Find the Surface Area of a Solid Objective: (12.1) Choose Appropriate Metric Measurement 4) A Objective: (12.3) Find the Surface Area of a Solid 24) D 5) C Objective: (12.1) Estimate the Mass of Object Objective: (12.2) Solve Apps: Perimeter and Area 25) C 6) A Objective: (12.1) Choose Appropriate Metric Measurement Objective: (12.3) Solve Apps: Ratio of Volumes/Surface Areas 26) D 7) B Objective: (12.1) Estimate the Mass of Object Objective: (12.3) Find Ratio of Volumes/Surface Areas 27) C 8) C Objective: (12.1) Choose Appropriate Metric Measurement Objective: (12.3) Solve Apps: Ratio of Volumes/Surface Areas 28) A 9) D Objective: (12.3) Solve Apps: Surface Area Objective: (12.3) Find Ratio of Volumes/Surface Areas 29) C 10) C Objective: (12.3) Solve Apps: Volume I Objective: (12.3) Find Ratio of Volumes/Surface Areas 30) A 11) C Objective: (12.3) Solve Apps: Volume I Objective: (12.3) Find Ratio of Volumes/Surface Areas 31) D 12) B Objective: (12.3) Solve Apps: Surface Area Objective: (12.3) Find Surface Area or Volume of Composite Solids 32) C Objective: (12.3) Solve Apps: Volume I 13) C 33) A Objective: (12.3) Find Surface Area or Volume of Composite Solids Objective: (12.3) Solve Apps: Surface Area 14) A 34) A Objective: (12.3) Find Surface Area or Volume of Composite Solids Objective: (12.2) Find Circumference of Circle 35) B 15) C Objective: (12.2) Find Circumference of Circle Objective: (12.2) Solve Apps: Perimeter and Area 36) D 16) B Objective: (12.2) Find Circumference of Circle Objective: (12.2) Solve Apps: Perimeter and Area 37) B 17) A Objective: (12.2) Find Circumference of Circle Objective: (12.3) Solve Apps: Ratio of Volumes/Surface Areas 38) C Objective: (12.2) Find Circumference of Circle 18) A 39) D Objective: (12.3) Solve Apps: Ratio of Volumes/Surface Areas Objective: (12.2) Find Circumference of Circle 40) A 19) C Objective: (12.2) Find Circumference of Circle Objective: (12.2) Solve Apps: Perimeter and Area 41) C 20) B Objective: (12.2) Find Circumference of Circle Objective: (12.1) Estimate the Mass of Object 42) C Objective: (12.2) Find Perimeter of Polygon 1 Answer Key Testname: 3162-UNIT-3-PRE-TEST 43) B 65) C Objective: (12.2) Find Perimeter of Polygon Objective: (12.3) Find the Volume of a Solid 44) C 66) B Objective: (12.2) Find Perimeter of Polygon Objective: (12.1) Convert Between English Units 45) D 67) C Objective: (12.2) Find Perimeter of Polygon Objective: (12.1) Convert Between Metric Units 46) A 68) B Objective: (12.1) Solve Apps: Mass and Temperature Objective: (12.1) Convert Between English Units 47) B 69) A Objective: (12.1) Solve Apps: Mass and Temperature Objective: (12.1) Convert Between English Units 48) D 70) B Objective: (12.1) Solve Apps: Mass and Temperature Objective: (12.1) Convert Between English Units 49) C 71) C Objective: (12.1) Solve Apps: Mass and Temperature Objective: (12.1) Convert Between Metric Units 50) C 72) C Objective: (12.1) Convert Between Metric and English Units I Objective: (12.1) Convert Between English Units 73) A 51) D Objective: (12.1) Convert Between Metric Units Objective: (12.1) Convert Between Metric and English Units I 74) B Objective: (12.1) Convert Between Metric Units 52) C 75) D Objective: (12.1) Convert Between Metric and English Units I Objective: (12.1) Convert Between English Units 76) D 53) D Objective: (12.1) Convert Between Metric Units Objective: (12.1) Convert Between Metric and English Units I 77) B Objective: (12.1) Convert Between English Units 54) A 78) D Objective: (12.2) Find Area of Circle Objective: (12.1) Convert Between English Units 55) D 79) B Objective: (12.2) Find Area of Circle Objective: (12.2) Find Area of Figure 56) D 80) B Objective: (12.2) Find Area of Circle Objective: (12.2) Find Area of Figure 57) B 81) B Objective: (12.2) Find Area of Circle Objective: (12.2) Find Area of Figure 58) C 82) D Objective: (12.2) Find Area of Polygon Objective: (12.2) Find Area of Figure 59) A 83) A Objective: (12.2) Find Area of Polygon Objective: (12.1) Identify Reasonable Measurement 60) B 84) D Objective: (12.2) Find Area of Polygon Objective: (12.1) Identify Reasonable Measurement 61) C 85) A Objective: (12.2) Find Area of Polygon Objective: (12.1) Identify Reasonable Measurement 62) B 86) A Objective: (12.3) Find the Volume of a Solid Objective: (12.1) Identify Reasonable Measurement 63) D 87) D Objective: (12.3) Find the Volume of a Solid Objective: (12.1) Convert Between Fahrenheit and Celsius 64) A Objective: (12.3) Find the Volume of a Solid 2 Answer Key Testname: 3162-UNIT-3-PRE-TEST 88) C Objective: (12.1) Convert Between Fahrenheit and Celsius 89) D Objective: (12.1) Convert Between Fahrenheit and Celsius 90) B Objective: (12.1) Convert Between Fahrenheit and Celsius 91) B Objective: (12.1) Convert Between Metric and English Units II 92) B Objective: (12.1) Convert Between Metric and English Units II 93) B Objective: (12.1) Convert Between Metric and English Units II 94) A Objective: (12.1) Convert Between Metric and English Units II 95) C Objective: (12.1) Determine Appropriate Unit of Mass 96) B Objective: (12.1) Determine Appropriate Unit of Mass 97) A Objective: (12.1) Determine Appropriate Unit of Mass 98) A Objective: (12.3) Solve Apps: Volume II 99) B Objective: (12.3) Solve Apps: Volume II 100) A Objective: (12.3) Solve Apps: Volume II 3
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