perimeter, circumference, area, volume Competency 9

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1 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 C = F A. 4.8 F C F B F D 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

2 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 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 minutes C. 6.1 minutes B minutes D minutes Find the circumference of each circle. Round to the nearest tenth. 8. The diameter is 21.8 cm. A cm C. 137 cm B cm D 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 mm 2 C mm 2 B. 29 mm 2 D. 43 mm 2 2

3 Name: ID: A Find the volume of each solid. Round to the nearest tenth if necessary. 11. A mm 3 C mm 3 B mm 3 D mm A cm 3 C cm 3 B cm 3 D. 133 cm 3 3

4 Name: ID: A 13. A. 300 ft 3 C. 110 ft 3 B. 80 ft 3 D. 100 ft A yd 3 C yd 3 B yd 3 D 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 cubic inches D. 17,157.3 cubic inches 4

5 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 cube: edge length, 7.9 ft 18. A. 493 ft 2 C ft 2 B ft 2 D ft 2 Find the surface area of each solid. Round to the nearest tenth if necessary. A mm 2 C mm 2 B mm 2 D. 492 mm cylinder: radius 6.9 ft; height 12.1 ft A ft 2 C ft 2 B ft 2 D ft 2 5

6 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

7 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 Substitute the value of C and simplify 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 boxes ææææ Æ 9 æææ boxes Æ æ 4 Æ æ 1 Æ 1

8 6. ANS: B Draw a Venn diagram to represent the situation. The number of salads bought will add up to 57, so = 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

9 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 m 2 Triangle: A = 1 2 bh A = 1 2 (5.6)(4.9) A = m 2 Total area: ª 26.0 m 2 3

10 11. ANS: D Use the formula V = Bh. V = (9)(5)(13) = 585 cm ANS: B Use the formula V = Bh. V = pr 2 h V = p(5 2 )(7.4) V = p(185) ª km 3 4

11 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 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 ft ANS: A The volume of a sphere is four thirds the product of p and the cube of the radius. 5

12 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 = = 478 cm 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 = ft ANS: D Use the formula SA = 2p r 2 + 2p rh. SA = 2p(5.2 2 ) + 2p(5.2)(7.8) SA = 54.08p p SA ª in 2 6

13 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 p SA ª m 2 SHORT ANSWER 1. ANS: 21 km Sample answer: 1.6 ª miles per hour = = 7.5 km per hour In 3 hours, Bern can run = 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: cm in. = cm. Then compare the three heights in centimeters: 152 > 149 > in. MSC: CAHSEE 7