Review Unit 1. Multiple Choice Identify the choice that best completes the statement or answers the question.

Transcription

1 Review Unit 1 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Which referent could you use for 1 m? a. The width of a computer keyboard b. The length of a dinner fork c. The length of your stride d. The width of a classroom in your school 2. Which referent could you use for 1 km? a. The distance equal to laps on an oval running track b. The length of an ipod c. The length of a snowboard d. The length of your arm span 3. Which referent could you use for 1 mm? a. The width of the head of an ant b. The diameter of a beach ball c. The distance between British Columbia and Manitoba d. The length of a sheet of loose-leaf paper 4. Which referent could you use for 1 in.? a. The distance from where you are now to the nearest restaurant b. The diameter of a bicycle wheel c. The length of your calculator d. The width of your largest toe 5. Which referent could you use for 1 ft.? a. The distance between Regina and Whitehorse b. The diameter of a basketball c. The height of your math teacher d. The height of an ice hockey net 6. Which imperial unit is most appropriate for measuring the length of a ladder? a. Feet b. Yards c. Miles d. Inches 7. Convert 3000 yd. to the nearest tenth of a metre. a m b m c m d m 8. The bobsled track at the Canada Olympic Park in Calgary is 1475 m long. What is this length to the nearest yard? a yd. b yd. c yd. d yd. 9. Determine the surface area of this right cone to the nearest square metre. 5 m 3 m a. 74 m 2 b. 55 m 2 c. 75 m 2 d. 83 m 2

2 10. A right rectangular pyramid has base dimensions 8 ft. by 6 ft. and a height of 12 ft. Calculate the surface area of the pyramid to the nearest square foot. a. 223 square feet b. 159 square feet c. 271 square feet d. 216 square feet 11. A right cone has a height of 13 cm and a base diameter of 17 cm. Determine the surface area of the cone to the nearest square centimetre. a. 642 cm 2 b. 574 cm 2 c. 415 cm 2 d cm A right cylindrical can has a volume of cm 3. What is the volume of a right cone with the same base and the same height, to the nearest tenth of a centimetre? a cm b cm c cm d cm 13. The circumference of a beach ball is 55 cm. Determine its volume to the nearest cubic centimetre. a cm 3 b. 963 cm 3 c. 307 cm 3 d cm A china bowl approximates a hemisphere with diameter 30 cm. One cup is 250 ml. How many cups are required to completely fill the bowl? a. 30 cups b. 28 cups c. 29 cups d. 9 cups Short Answer 15. Convert 5 yd. 6 in. to inches. 16. A cruise ship is 790 ft. long. Convert this length to the nearest metre. 17. A hemisphere has radius 7 ft. Determine the surface area of the hemisphere to the nearest square foot. 18. A spherical balloon has a surface area of 88 cm 2. What is the diameter of the balloon to the nearest tenth of a centimetre? 19. Each layer of a three-layer wedding cake is a cylinder with height 8 cm. The bottom layer has diameter 24 cm, the middle layer has diameter 19 cm, and the top layer has diameter 14 cm. The cake is covered in frosting. Determine the area of frosting to the nearest square centimetre. Problem 20. A nautical mile is approximately 6080 ft. Convert 6 nautical miles to the nearest tenth of a kilometre. 21. Determine the surface area of this composite object, which is a right square prism and a right square pyramid, to the nearest square foot. Explain your answer. 3 ft. 9 ft. 6 ft. 6 ft.

3 22. This cone was cut from a right rectangular prism with dimensions 19 cm by 21 cm by 65 cm. What volume of the right rectangular prism, in cubic centimetres, remains? 10 cm 35 cm 23. A sculpture comprises a right rectangular prism with base dimensions 29 m by 33 m, and height 15 m. A right cylinder with base diameter 7 m and height 14 m sits on top of the prism. a) Determine the volume of the sculpture to the nearest cubic metre. b) Determine the surface area of the sculpture to the nearest square metre. 24. A fathom is a unit of length used to measure the depth of water. A fathom is equal to 6 ft. a) How many fathoms are in a mile? b) Challenger Deep in the Pacific Ocean is the deepest point in Earth s oceans. It is ft. below sea level. What is this depth to the nearest fathom? Is this depth greater than or less than 7 mi.? Explain.

4 Review Unit 1 Answer Section MULTIPLE CHOICE 1. ANS: C PTS: 1 DIF: Easy REF: 1.2 Measuring Length and Distance LOC: 10.M1 KEY: Conceptual Understanding 2. ANS: A PTS: 1 DIF: Easy REF: 1.2 Measuring Length and Distance LOC: 10.M1 KEY: Conceptual Understanding 3. ANS: A PTS: 1 DIF: Easy REF: 1.2 Measuring Length and Distance LOC: 10.M1 KEY: Conceptual Understanding 4. ANS: D PTS: 1 DIF: Easy REF: 1.2 Measuring Length and Distance LOC: 10.M1 KEY: Conceptual Understanding 5. ANS: B PTS: 1 DIF: Easy REF: 1.2 Measuring Length and Distance LOC: 10.M1 KEY: Conceptual Understanding 6. ANS: A PTS: 1 DIF: Easy REF: 1.2 Measuring Length and Distance LOC: 10.M1 KEY: Conceptual Understanding 7. ANS: C PTS: 1 DIF: Easy REF: 1.3 Relating SI and Imperial Units LOC: 10.M2 8. ANS: A PTS: 1 DIF: Moderate REF: 1.3 Relating SI and Imperial Units LOC: 10.M2 9. ANS: D PTS: 1 DIF: Moderate REF: 1.4 Surface Areas of Right Pyramids and Right Cones LOC: 10.M3 10. ANS: A PTS: 1 DIF: Moderate REF: 1.4 Surface Areas of Right Pyramids and Right Cones LOC: 10.M3 11. ANS: A PTS: 1 DIF: Moderate REF: 1.4 Surface Areas of Right Pyramids and Right Cones LOC: 10.M3 12. ANS: D PTS: 1 DIF: Moderate REF: 1.5 Volumes of Right Pyramids and Right Cones LOC: 10.M3 13. ANS: D PTS: 1 DIF: Moderate REF: 1.6 Surface Area and Volume of a Sphere LOC: 10.M3 14. ANS: C PTS: 1 DIF: Difficult REF: 1.6 Surface Area and Volume of a Sphere LOC: 10.M3 SHORT ANSWER 15. ANS: 186 in. PTS: 1 DIF: Easy REF: 1.1 Imperial Measures of Length LOC: 10.M2

5 16. ANS: 237 m PTS: 1 DIF: Easy REF: 1.3 Relating SI and Imperial Units LOC: 10.M2 17. ANS: 462 square feet PTS: 1 DIF: Easy REF: 1.6 Surface Area and Volume of a Sphere LOC: 10.M3 18. ANS: 5.3 cm PTS: 1 DIF: Moderate REF: 1.6 Surface Area and Volume of a Sphere LOC: 10.M3 19. ANS: 1885 cm 2 PTS: 1 DIF: Difficult REF: 1.7 Solving Problems Involving Objects LOC: 10.M3 PROBLEM 20. ANS: Convert 6 nautical miles to feet. Convert ft. to metres. Convert m to kilometres. So, 6 nautical miles is approximately 10.9 km. PTS: 1 DIF: Moderate REF: 1.3 Relating SI and Imperial Units LOC: 10.M2 KEY: Problem-Solving Skills 21. ANS:

6 The surface area of the composite object is: area of the 4 rectangular faces of the prism + area of square base of the prism + area of 4 triangular faces of the pyramid The area of the 4 rectangular faces of the prism, in square feet, is: The area of the square base of the prism, in square feet, is: To determine the surface area of the triangular faces, calculate the slant height, s. Sketch a triangle to represent a triangular face. A 3 ft. s C D B 6 ft. Use the Pythagorean Theorem in right ADB. The area of the 4 triangular faces of the pyramid, in square feet, is: The surface area of the composite object, in square feet, is: The surface area of the composite object is approximately 303 square feet. PTS: 1 DIF: Difficult REF: 1.7 Solving Problems Involving Objects LOC: 10.M3 KEY: Communication Problem-Solving Skills 22. ANS: Volume remaining = volume of rectangular prism volume of cone Use the formula for the volume of a right rectangular prism.

7 Use the formula for the volume of a right cone. The radius, r, is: The volume of the right rectangular prism that remains is: The volume of the right rectangular prism that remains is approximately cm 3. PTS: 1 DIF: Difficult REF: 1.7 Solving Problems Involving Objects LOC: 10.M3 KEY: Problem-Solving Skills 23. ANS: a) Volume of sculpture = volume of prism + volume of cylinder Use the formula for the volume of a right rectangular prism. Use the formula for the volume of a right cylinder. The radius, r, is: The volume of the sculpture is: The volume of the sculpture is approximately m 3. b) The surface area of the sculpture is the sum of the areas of the faces of the right rectangular prism and the curved surface of the cylinder.

8 The area of the rectangular faces of the prism, in square metres, is: The area of the rectangular bases of the prism, in square metres, is: Use the formula to find the area of the curved surface of the cylinder. The radius, r, is: The surface area of the sculpture is: The surface area of the sculpture is approximately 4082 m 2. PTS: 1 DIF: Difficult REF: 1.7 Solving Problems Involving Objects LOC: 10.M3 KEY: Problem-Solving Skills 24. ANS: a) 1 mi. = 5280 ft. and 1 fathom = 6 ft. So, 1 mi. = fathoms 1 mi. = 880 fathoms So, there are 880 fathoms in a mile. b) To convert feet to fathoms, divide by ft. = fathoms ft. = fathoms The depth at Challenger Deep is approximately 5966 fathoms. Since 1 mi. = 880 fathoms, 7 mi. is: 7(880 fathoms) = 6160 fathoms Since 5966 fathoms is less than 6160 fathoms, the depth at Challenger Deep is less than 7 mi. PTS: 1 DIF: Difficult REF: 1.1 Imperial Measures of Length LOC: 10.M2 KEY: Communication Problem-Solving Skills