Name: Class: _ Date: _ ID: A perimeter, circumference, area, volume Competency 9 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. A fountain is set up at the center of a circular garden whose circumference is 32 ft. Solve the equation C = 2pr for r. Then find the radius of the garden to the nearest tenth. A. r = 2C p ; 5.1 ft C. r = C ; 20.4 ft 2p B. r = 2C p ; 20.4 ft D. r = C ; 5.1 ft 2p 2. Mona runs at an average speed of 3 yards per second. Solve the equation S = d t her to run 170 yards? Round to the nearest tenth. for t. How long will take A. t = d ; 56.7 sec C. t = d s; 56.7 sec S B. t = d ; 510 yards D. t = d s; 510 yards S Complete each conversion. Round your answer to the nearest hundredth if necessary. 3. -29 C = F A. 4.8 F C. 48.11 F B. 84.2 F D. 20.2 F Solve using the draw-a-diagram strategy. 4. A sink is being filled with water. After 15 seconds the sink is 1 4 the sink if the water rate is constant? full. How much longer will it take to fill A. 30 seconds C. 1 minute B. 45 seconds D. 1 minute 15 seconds 5. Jamal is stacking boxes of books for the library book sale. Each box contains 24 books. If the stack of boxes is in the shape of a square-based pyramid, how many books total will there be in a stack of 4 layers? A. 720 C. 30 B. 336 D. 28 1
Name: ID: A 6. At lunch, 62 students order hamburgers, 57 ordered salads, and 73 ordered french fries. Thirty-two students ordered both hamburgers and fries, 22 ordered fries and a salad, while 16 students all three. No students ordered a hamburger and salad. How many students bought just salad? A. 57 C. 19 B. 35 D. 17 7. It takes Steve 14 minutes to cut 3.5 yards of fabric. How long will it take to cut a similar piece of fabric that is 5.8 yards? A. 23.2 minutes C. 6.1 minutes B. 11.6 minutes D. 1.45 minutes Find the circumference of each circle. Round to the nearest tenth. 8. The diameter is 21.8 cm. A. 17.1 cm C. 137 cm B. 68.5 cm D. 21.8 cm 9. Tony makes a rectangle using 12 blocks. What number of blocks should the length and width of the rectangle be? All 12 blocks are used. A. l = 4 blocks, w = 3 blocks C. l = 5 blocks, w = 3 blocks B. l = 4 blocks, w = 2 blocks D. l = 3 blocks, w = 3 blocks Find the area of each figure. Round to the nearest tenth if necessary. 10. A. 23.2 mm 2 C. 44.1 mm 2 B. 29 mm 2 D. 43 mm 2 2
Name: ID: A Find the volume of each solid. Round to the nearest tenth if necessary. 11. A. 154.4 mm 3 C. 23.8 mm 3 B. 694.7 mm 3 D. 308.7 mm 3 12. A. 1046.4 cm 3 C. 266.1 cm 3 B. 731.8 cm 3 D. 133 cm 3 3
Name: ID: A 13. A. 300 ft 3 C. 110 ft 3 B. 80 ft 3 D. 100 ft 3 14. A. 2111.2 yd 3 C. 1583.4 yd 3 B. 527.8 yd 3 D. 422.2 yd 3 Find the volume of each sphere. Round to the nearest tenth, if necessary. 15. A. 2,144.7 cubic inches C. 1,072.3 cubic inches B. 268.1 cubic inches D. 17,157.3 cubic inches 4
Name: ID: A Find the surface area of each solid. Round to the nearest tenth if necessary. 16. A. 664 yd 2 C. 332 yd 2 B. 796 yd 2 D. 128 yd 2 17. cube: edge length, 7.9 ft 18. A. 493 ft 2 C. 303.3 ft 2 B. 374.5 ft 2 D. 94.8 ft 2 Find the surface area of each solid. Round to the nearest tenth if necessary. A. 337.6 mm 2 C. 342.7 mm 2 B. 1850.5 mm 2 D. 492 mm 2 19. cylinder: radius 6.9 ft; height 12.1 ft A. 823.7 ft 2 C. 1070.8 ft 2 B. 561.4 ft 2 D. 567.9 ft 2 5
Name: ID: A Short Answer Determine reasonable answers to solve the problems. 1. One mile is approximately equal to 1.6 kilometers. Bern runs 5 miles in an hour. Can he run 14 km, 21 km, or 29 km in 3 hours? Explain. 2. Matt is 58 inches tall. DeShawn is 152 centimeters tall. Sophie is 149 centimeters tall. Order the students from tallest to shortest. 6
perimeter, circumference, area, volume Competency 9 Answer Section MULTIPLE CHOICE 1. ANS: D Apply the Division Property of Equality to C = 2pr and simplify it to solve for r. Substitute the value of C and p in the new equation and calculate the radius. 2. ANS: A Apply the Division and Multiplication Properties of Equality to S = d and simplify it to solve for t. t Substitute the value of d and S in the new equation and calculate the time, t. 3. ANS: D Use the equation F = 9 C + 32. Substitute the value of C and simplify. 5 4. ANS: B Draw a figure to represent the sink. Divide it into 4 parts. If it takes 15 seconds to fill 1 of the 4 parts, how long will it take to fill the remaining 3 parts? 1 4 = 15 seconds 5. ANS: A Draw a figure to represent the square-based pyramid stack of books. Each layer will be a perfect square. Add up the number of boxes, and multiply each box by 24. 16 boxes ææææ Æ 9 æææ boxes Æ æ 4 Æ æ 1 Æ 1
6. ANS: B Draw a Venn diagram to represent the situation. The number of salads bought will add up to 57, so 57 16 6 = 35. 7. ANS: A Draw a diagram to represent the situation. Since 1 yd of fabric are cut in 4 minutes, multiply 5.8 by 4 to see how long it will take to cut 5.8 yards. 14 min = 3.5 yds 12 min = 3 yds 10 min = 2.5 yds 8 min = 2 yds 6 min = 1.5 yds 4 min = 1 yds 8. ANS: B The diameter is 12.9 km. Use the formula C = pd. C = p(12.9) C ª 40.5 km 9. ANS: A Make a model to ensure that the length and width actually make a rectangle with exactly 12 blocks. 2
10. ANS: B Find the area of the triangle and the area of the semicircle. The total area will be the sum of these two areas. Semicircle: A = 1 2 pr2 A = 1 p Ê 5.6 ˆ 2 2 ËÁ 2 A = 1 p( 2.8) 2 2 A = 1 2 p(7.84) ª 12.32 m 2 Triangle: A = 1 2 bh A = 1 2 (5.6)(4.9) A = 13.72 m 2 Total area: 13.72 + 12.32 ª 26.0 m 2 3
11. ANS: D Use the formula V = Bh. V = (9)(5)(13) = 585 cm 3 12. ANS: B Use the formula V = Bh. V = pr 2 h V = p(5 2 )(7.4) V = p(185) ª 581.2 km 3 4
13. ANS: D Use the formula V = 1 3 Bh. V = 1 3 Bh V = 1 (5 4)(11) 3 V = 1 3 (220) ª 73.3 in 3 14. ANS: B Use the formula V = 1 3 Bh. V = 1 3 pr2 h V = 1 3 p(6 2 )(13) V = p(156) ª 490.1 ft 3 15. ANS: A The volume of a sphere is four thirds the product of p and the cube of the radius. 5
16. ANS: A Find the area of each of the six faces. Add these together to find the total surface area. SA = 2(11)(9) + 2(9)(7) + 2(11)(7) SA = 198 + 126 + 154 = 478 cm 2 17. ANS: B cube: edge length, 11.5 ft Find the area of each of the six faces. Add these together to find the total surface area. In the case of a cube, each face has the same area. SA = 6(11.5)(11.5) SA = 793.5 ft 2 18. ANS: D Use the formula SA = 2p r 2 + 2p rh. SA = 2p(5.2 2 ) + 2p(5.2)(7.8) SA = 54.08p + 81.12p SA ª 424.7 in 2 6
19. ANS: A cylinder: radius 4.8 m; height 10.2 m Use the formula SA = 2p r 2 + 2p rh. SA = 2p(4.8 2 ) + 2p(4.8)(10.2) SA = 46.08p + 97.92p SA ª 452.4 m 2 SHORT ANSWER 1. ANS: 21 km Sample answer: 1.6 ª 1.5 5 miles per hour = 5 1.5 = 7.5 km per hour In 3 hours, Bern can run 3 7.5 = 22.5 km, which is closer to 21 km. 2. ANS: DeShawn, Sophie, Matt To compare the heights, multiply the number of inches by the conversion factor: 58 2.54 cm in. = 147.32 cm. Then compare the three heights in centimeters: 152 > 149 > 147.32. 1 in. MSC: CAHSEE 7