UNIT 3 - MEASUREMENT & PROPORTIONAL REASONING TEST

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1 Class: Date: UNIT 3 - MEASUREMENT & PROPORTIONAL REASONING TEST Multiple Choice Identify the choice that best completes the statement or answers the question. 1. When designing a building, you must be sure that the building can withstand hurricane-force winds, which have a velocity of 74 mi/h or more. The formula F = 0.004Av 2 gives the force F in pounds exerted by a wind blowing against a flat surface. A is the area of the surface in square feet, and v is the wind velocity in miles per hour. How much force is exerted by a wind blowing at 91 mi/h against the side of the building shown? A. about 6 tons B. about 62 tons C. about 26 tons D. about 12,461 tons Short Answer - SHOW ALL YOUR WORK! 2. Find the area. The figure is not drawn to scale. 3. The area of a parallelogram is 280 cm 2 and the height is 35 cm. Find the corresponding base. 1

2 Find the area of a parallelogram with the given vertices. 4. P( 2, 5), Q(9, 5), R(1, 5), S(12, 5) Find the area of the trapezoid. Leave your answer in simplest radical form A kite has diagonals 5.8 ft and 6 ft. What is the area of the kite? 7. The area of a regular hexagon is 50 in. 2 Find the length of a side. Round your answer to the nearest tenth. 8. The figures are similar. Give the ratio of the perimeters and the ratio of the areas of the first figure to the second. The figures are not drawn to scale. 2

3 The area of a regular octagon (octagon has 8 sides) is 35 cm 2. What is the area of a regular octagon with sides five times as long? 11. A rectangular napkin costs $3.25. A similar tablecloth is five times longer and five times wider. How much would you expect to pay for the tablecloth? 12. Hiram raises earthworms. In a square of compost 4 ft by 4 ft, he can have 1000 earthworms. How many earthworms can he have if his square of compost has a side length that is 8 times longer? Find the area of the regular polygon. (Use A = 0.5 n s a, where n = the number of sides, s = lentgh of a side, and a = the apothem - height from radius). Give the answer to the nearest tenth. 13. Decagon (decagon has 10 sides) with a side of 4 cm 14. Dodecagon (dodecagon has 12 sides) with a perimeter of 108 cm 15. Hexagon (hexagon has 6 sides) with a radius of 5 in. 16. The Ruffs are planning to buy an above-ground swimming pool shaped as a regular octagon (octagon has 8 sides). The radius of the octagon is 9 feet. To the nearest tenth, find the area of the surface of the water in the pool. 3

4 17. The figure represents the overhead view of a deck surrounding a hot tub. What is the area of the deck? Round to the nearest tenth. 18. Find the area of the circle. Leave your answer in terms of π. 19. Find the area of the shaded portion of the figure. Dimensions are in feet. Leave your answer in terms of π. The figure is not drawn to scale. 4

5 20. The delivery van arrives at an office every day between 3 PM and 5 PM. The office doors were locked between 3:15 PM and 3:35 PM. What is the probability that the doors were unlocked when the delivery van arrived? 21. The radius of the bull s-eye of the dartboard is 8 inches. The radius of each concentric circle is 8 inches more than the radius of the circle inside it. If a dart lands at random on the dartboard, what is the probability that the dart will hit in area C? 22. Allison is planning to cover the lateral surface of a large cylindrical garbage can with decorative fabric for a theme party. The can has a diameter of 3 feet and a height of 3.5 feet. How much fabric does she need? Round to the nearest square foot. 23. Find the surface area of the regular pyramid shown to the nearest whole number. 5

6 24. Find the lateral area of a regular pentagonal (pentagon has 5 sides) pyramid that has a slant height of 14 in. and a base side length of 6 in. 25. Find the surface area of the cone to the nearest tenth. 26. Find the surface area of a conical grain storage tank that has a height of 41 meters and a diameter of 16 meters. Round the answer to the nearest square meter. 27. Find the surface area of the cone in terms of π. 6

7 Find the volume of the square pyramid shown. Round to the nearest tenth if necessary Find the volume of the oblique cone shown. Round to the nearest tenth. Find the surface area of the sphere with the given dimension. Leave your answer in terms of π. 30. Diameter of 14 cm 7

8 31. A balloon has a circumference of 11 cm. Use the circumference to approximate the surface area of the balloon to the nearest square centimeter. 32. Find the volume of the sphere shown. Give each answer rounded to the nearest cubic unit. 33. The volume of a sphere is 5000π m 3. What is the surface area of the sphere to the nearest square meter? 34. Are the two figures similar? If so, give the similarity ratio of the smaller figure to the larger figure. 8

9 35. A chain fits tightly around two gears as shown. The distance between the centers of the gears is 37 inches. The radius of the larger gear is 13 inches. Find the radius of the smaller gear. Round your answer to the nearest tenth, if necessary. The diagram is not to scale. Problems 36 through 50 are Constructed Respond. You must SHOW ALL YOUR WORK! 36. Your neighbor s pool is shaped like an oval with two straight sides and two circular edges. The measurements are given in the diagram to the left. Find the area of the pool and the distance around the pool. The area of the Pool = The distance around the Pool = 9

10 37. Identify and Calculate the Area & Perimeter for the Quadrilateral. a1 = 9.7 inches b1 = inches h = 4.6 inches a2 = 3.4 inches b2 = 4.98 inches Type: Area: Perimeter: 38. Identify and calculate the area and perimeter of the polygon. a = 5.6 ft c = 9.4 ft h = 5.3 ft Type: Area: Perimeter: 10

11 39. Identify and calculate the area and perimeter of the polygon. a = 7.6 cm b= 4.7 cm c = 8.94 cm Type: Area: Perimeter: 40. A jet travels 510 miles in 2 hours. At this rate, how far could the jet fly in 12 hours? What is the rate of speed of the jet 11

12 Use the following figure for problems Find the vertical height of the bowl of glass 3. Show your work. Height: 12

13 Calculate the volume of the bowl of each of these glasses. Round to the tenth, and write the appropriate unit(s). Show all your work. 42. Glass 1: Volume = 43. Glass 2: Volume = 13

14 44. Glass 3: Volume = 45. Find the height of liquid in Glass 1 when it is half full. Show all your work. Height of the liquid: 14

15 Use the following information for problems Show all your work. My sister s birthday is in a few weeks and I would like to buy her a new vase to keep fresh flowers in her house. She often forgets to water her flowers and needs a vase that holds a lot of water. In a catalog there are three vases available and I want to purchase the one that holds the most water. The first vase is a cylinder with diameter 10 cm and height 40 cm. The second vase is a cone with base diameter 16 cm and height 45 cm. The third vase is a sphere with diameter 18 cm. Round to the nearest whole number. 46. Which vase should I purchase, and what is it s volume? I should purchase the vase, and it s volume is. 47. How much more water does the largest vase hold than the smallest vase? Answer: 15

16 48. Suppose the diameter of each vase decreases by 2 cm. Which vase would hold the most water? Answer: 49. The vase company designs a new vase that is shaped like a cylinder on bottom and a cone on top. The catalog states that the width is 12 cm and the total height is 42 cm. What would the height of the cylinder part have to be in order for the total volume to be 1224π cm 3? The height of the cylinder part have to be. 16

17 50. Design a composite vase with two of shapes, above. Place the sphere on bottom and the cylinder on top then determine the volume. Increase the diameter of the sphere by 2. 17

18 UNIT 3 - MEASUREMENT & PROPORTIONAL REASONING TEST Answer Section MULTIPLE CHOICE 1. ANS: A DIF: L4 REF: 10-1 Areas of Parallelograms and Triangles SHORT ANSWER 2. ANS: cm 2 DIF: L3 REF: 10-1 Areas of Parallelograms and Triangles 3. ANS: 8 cm DIF: L3 REF: 10-1 Areas of Parallelograms and Triangles 4. ANS: 110 units 2 DIF: L4 REF: 10-1 Areas of Parallelograms and Triangles 5. ANS: 78 ft 2 DIF: L3 REF: 10-2 Areas of Trapezoids, Rhombuses, and Kites 6. ANS: 17.4 ft 2 DIF: L3 REF: 10-2 Areas of Trapezoids, Rhombuses, and Kites 7. ANS: 4.4 in. DIF: L4 REF: 10-3 Areas of Regular Polygons 8. ANS: 9 81 and 8 64 DIF: L3 REF: 10-4 Perimeters and Areas of Similar Figures 9. ANS: 4 : 7 and 16 : 49 DIF: L3 REF: 10-4 Perimeters and Areas of Similar Figures 1

19 10. ANS: 875 cm 2 DIF: L4 REF: 10-4 Perimeters and Areas of Similar Figures 11. ANS: $81.25 DIF: L3 REF: 10-4 Perimeters and Areas of Similar Figures 12. ANS: 64,000 DIF: L3 REF: 10-4 Perimeters and Areas of Similar Figures 13. ANS: cm 2 DIF: L3 REF: 10-5 Trigonometry and Area 14. ANS: cm 2 DIF: L4 REF: 10-5 Trigonometry and Area 15. ANS: 65.0 in. 2 DIF: L3 REF: 10-5 Trigonometry and Area 16. ANS: ft 2 DIF: L3 REF: 10-5 Trigonometry and Area 17. ANS: 52.5 m 2 DIF: L4 REF: 10-7 Areas of Circles and Sectors 18. ANS: 4.84π m 2 DIF: L3 REF: 10-7 Areas of Circles and Sectors 19. ANS: ( 68 16π) ft 2 DIF: L4 REF: 10-7 Areas of Circles and Sectors 20. ANS: 5 6 DIF: L4 REF: 10-8 Geometric Probability 2

20 21. ANS: 5 16 DIF: L3 REF: 10-8 Geometric Probability 22. ANS: 33 ft 2 DIF: L3 REF: 11-2 Surface Areas of Prisms and Cylinders 23. ANS: 95 ft 2 DIF: L3 REF: 11-3 Surface Areas of Pyramids and Cones 24. ANS: 210 in. 2 DIF: L3 REF: 11-3 Surface Areas of Pyramids and Cones 25. ANS: cm 2 DIF: L3 REF: 11-3 Surface Areas of Pyramids and Cones 26. ANS: 1251 m 2 DIF: L3 REF: 11-3 Surface Areas of Pyramids and Cones 27. ANS: 60π cm 2 DIF: L3 REF: 11-3 Surface Areas of Pyramids and Cones 28. ANS: 605 cm 3 DIF: L2 REF: 11-5 Volumes of Pyramids and Cones 29. ANS: in. 3 DIF: L3 REF: 11-5 Volumes of Pyramids and Cones 30. ANS: 196π cm 2 DIF: L3 REF: 11-6 Surface Areas and Volumes of Spheres 3

21 31. ANS: 39 cm 2 DIF: L3 REF: 11-6 Surface Areas and Volumes of Spheres 32. ANS: 1,437 cm 3 DIF: L3 REF: 11-6 Surface Areas and Volumes of Spheres 33. ANS: 3033 m 2 DIF: L3 REF: 11-6 Surface Areas and Volumes of Spheres 34. ANS: no DIF: L3 REF: 11-7 Areas and Volumes of Similar Solids 35. ANS: 4.5 inches DIF: L4 REF: 12-1 Tangent Lines 36. ANS: The figure can be separated into a central rectangle and a left and right semicircle. Note that the two semicircles are exactly the same as each other. This fact will be used later in the problem to find area and perimeter. The two semicircles have the same radius and can therefore be combined into one whole circle. The total area of the pool is equal to the sum of the areas of the rectangle and the circle to the right. Area of the rectangle: A = LW = 14 * 11 = 154 ft 2 Area of the circle: A = (pi)r 2 = (pi)8 2 = 64(pi) = ft 2 Total area: A = = ft 2 Total perimete: P = 2(14) + 2(11) + 2(3.14)(7) = =

22 37. ANS: 38. ANS: 39. ANS: 40. ANS: 510 mi/2 hrs = 255mi/hr (12 hrs)(255 mi/hr) 3,060 miles 41. ANS: Height: ANS: 118 cm ANS: 214 5

23 44. ANS: 47 cm ANS: Height of the liquid: 3.01 cm Shows work such as: 118/ 2 = 59 cm 3 (3.14)(2.5) 2 h = 59 cm h = 59 h = 3.01 cm 46. ANS: I should purchase the cylinder vase, and it s volume is _3142 cm 3. Cylinder: V = πr2h = π(5)2(40) = 1000π cm 3 = 3142 cm 3 Cone: V = 1 πr2h = 1 π(8)2(45) = 960π cm 3 = 3015 cm 3 Sphere: V = 4 πr3 = 4 π(9)3 = 972π cm 3 = 3054 cm 3 Purchase the cylindrical vase. 2. Volume of the cylinder vase - Volume 47. ANS: Volume of the cylinder vase - Volume of the cone vase 1000π - 940π = 40π cm 3 The cylinder vase holds cm 3 more water than the cone vase. 48. ANS: Cylinder: V = πr 2 h = π (4)2(40) = 640πcm 3 Cone: V = 1 πr 2 h = 1 π (7)2(45) = 735πcm 3 Sphere: V = 4 πr 3 = 4 π (8)3 = πcm 3 The cone vase would hold the most water. 6

24 49. ANS: π(6)2x + 1 π (6) 2 (42-x) = 1224π 36πx + 12π (42 - x) = 1224π 36πx + 504π - 12πx = 1224π 24πx = 720π x = 30 The cylinder part is 30 cm high. 50. ANS: Volume of a cylinder: V = r 2 h = (3.14)(25)(40) = r = 10/2 = 5 cm h = 40 cm Volume of a sphere: V = 4/3 r 3 = (4/3)(3.14)(1000) = r = (18+2)/2 = 10 Volume of composite vase: V = = cm 3 7