10.7 Solve Problems Using Logical Reasoning, pp. 360–361 4. 5. 6. 7. 9.

C Gregory yes 3 bananas Figure 4, Figure 3, Figure 1, Figure 2

Chapter Review, p. 365 1. a) /a and /c, /b and /d b) opposite angles 2. /1 5 /3 5 /5 5 /7 5 82°, /2 5 /4 5 /6 5 /8 5 98° 3. /b, /e, /p, and /s 4. 35° 5. a) yes b) rectangle c) The diagonals will not meet at a right angle. 6. e.g., 3 cm and 4 cm 7. a) 85° b) 8.1 cm 4.0 cm 50°

c) 15°

45°

7.0 cm

6.0 cm

6.0 cm

150°

d) 78°

12° 12°

Chapter Self-Test, p. 363 1. Join the points to form 2 chords. Then find the perpendicular bisector of each chord. The intersection of the perpendicular bisectors is the centre of the circle. 2. /a 5 138°, /b 5 42°, /c 5 138° 3. e.g.,

8. a) cyclist A b) a2 5 5.52 1 3.42, b2 5 3.42 1 5.02 c) Otherwise you cannot use the Pythagorean theorem

Math in Action: Theatre Technician, pp. 367–368 1. a) 2 2.

b) yes

c) /b 5 9° 54˚

45°

45°

4. a) 8 b) /3 and /6, /16 and /9 c) 360° 5. /a 5 81°, /b 5 25°, /c 5 74°, /d 5 25° 6. a) 45° b) 180° 2 98° 2 37° 5 45° c) obtuse and scalene 7. a) 94° 43°

126˚ 54˚

126˚

126˚ 54˚

3. Yes, the angles are 76°, 104°, 76°, and 104°, and each of these is within 15° of 90°. 5. 1.45 m 6. a) 40° b) 70°

43°

b) a rhombus and a chevron c) 90° 8. a) 5.7 m b) 12.0 cm 9. 10 cm 10. 2.01 km

500 Answers

54˚

126˚

Chapter 11, p. 369 Getting Started, p. 371 1. a) litres b) centimetres

c) square centimetres d) cubic centimetres NEL

2. a) e.g.,

9. 11. 12. 13.

4 cm 4 cm

a) about 188.9 m2 about 27 m2 about 603 cm2 about 113 cm2

b) about $175.00

11.3 Volume of a Cylinder, pp. 380–381 12 cm

a) e.g., about 300 m3 a) about 8204.0 cm3 a) e.g., about 96 cm3 a) about 1570.0 cm3 a) about 628 cm3 a) about 27.5 m3 b) about 27 500 L 10. e.g., about 846 cm3 11. about 220 cm3 12. 4. 5. 6. 7. 8. 9.

surface area 5 224 cm2 b) e.g., 5m 5m

Radius of base Diameter of base

4m

5. 6. 7. 8.

3 cm 3 cm

4 cm

2 cm

6.0 m

12.0 m

6.0 m

surface area 8 93 cm2 306 cm2 a) area 8 50.2 cm2, circumference 8 25.1 cm b) area 8 15.9 m2, circumference 8 14.1 m a) about 234.4 cm3 b) 36 cm3 a) 234.4 mL b) 36 mL a) 9 edges, 5 faces, 6 vertices b) 18 edges, 8 faces, 12 vertices e.g.,

3 cm

8 cm

3.5 cm

5m

3. 4.

4 cm

6 cm

2 cm

9 cm

7.0 cm 12.0 m

b) e.g., about 300 cm3 b) about 143.3 cm3 b) e.g., about 270 cm3 b) about 1570.0 mL b) about 40.9 m3 c) 550 min or about 9 h

Height 11 cm

Volume 553 cm3

5.0 m

565.2 m3

8.0 cm

307.7 cm3

2.0 m

226.1 m3

13. 14. 15. 16. 17.

about 10.0 cm about 8.0 cm a) about 6051.0 cm b) about 5000.8 cm cylinder cylinder with a diameter of 10.0 cm and a height of 7.0 cm 18. a) about 4.5 cm b) can of mushroom soup 19. Volume would quadruple. 20. e.g., 8.0 cm 3 8.0 cm 3 15.6 cm for the juice carton and a height of 12.7 cm with a radius of 5.0 cm for the water bottle

2 cm

11.4 Solve Problems Using Diagrams, p. 384 9. a) area of trapezoid 5 3560.0 cm2, 2 3. volume 8 8.8 m3, surface area 8 25.2 m2 area of rectangle 5 1683.0 cm b) volume of trapezoidal prism 5 1 352 800.0 cm3, 4. volume 8 11.6 m3, surface area 8 39.7 m2 7. a) b) about 1.4 m2 volume of rectangular prism 5 639 540.0 cm3 c) 1 992 340.0 cm3 11.2 Surface Area of a Cylinder, pp. 376–377 4. a) about 314 cm2 5. a) about 251 cm2 6. a) about 110.4 cm2 b) about 93.5 cm2 7. a) about 162.9 m2 b) about 2491.6 m2 NEL

2.5 m

b) about 184.3 cm2 b) about 353.3 cm2 c) about 126.3 cm2 c) about 201.0 cm2

0.5 m

Answers 501

9. 10. 11. 12.

200 squares 24 about 671 m 3.24 L

16. a) n 1 1 faces b) 2n edges c) n 1 1 vertices d) F 1 V 2 E 5 (n 1 1) 1 (n 1 1) 2 (2n) 52

Mid-Chapter Review, p. 387 1. a) about 301 cm2 c) about 1548.0 cm2 2 b) about 1059.8 cm d) about 16 485.0 cm2 2. about 2.8 m2 3. e.g., First, measure the height and the diameter of the roll. The surface area of the roll is twice the height multiplied by the circumference, or SA 5 2 3 h 3 2pr. 4. a) about 77 401 mm2 b) about 678.2 cm2 2 5. about 980 cm 6. a) about 10 613 cm3 c) about 6280 cm3 b) about 2653.3 cm3 7. about 22 078 mL 8. about 469.0 m3 9. about 13.3 L 10. largest container is about 9420 cm3, middlesized container is about 6280 cm3, small container is about 3140 cm3

11.6 Polyhedron Faces, Edges, and Vertices, pp. 392–393 3. 6 4. F 1 V 2 E 5 4 1 4 2 6 52 6. Number of faces Number of edges Number of vertices 6

9

5

6

12

8

6

11

7

20

30

12

16

24

10

8

12

6

12. b) 5 faces c) 9 edges d) 6 vertices 13. b) 6 faces c) 10 edges d) 6 vertices 14. F 1 V 2 E 5 8 1 6 2 12 52 15. a) n 1 2 faces b) 3n edges c) 2n vertices d) F 1 V 2 E 5 (n 1 2) 1 (2n) 2 (3n) 52

502 Answers

Chapter Self-Test, p. 395 1. For the larger candle:

For the smaller candle:

2. a, d 3. a) surface area 8 297 cm2, volume 8 382 cm3 b) surface area 8 517.5 cm2, volume 8 844.5 cm3 c) surface area 8 246.6 cm2, volume 8 212.3 cm3 d) surface area 8 376.8 cm2, volume 8 549.5 cm3 4. about 138.3 m3 5. about 785 cm3 6. Since the angle at each corner of a square is 90°, if more than three squares meet at a vertex, then the total interior angle of the vertex will be greater than or equal to 360°. This means that the shape would either be flat or turned upward, neither of which can make a polyhedron. So, no more than three congruent squares can meet at a vertex to form a Platonic solid because a Platonic solid must be a polyhedron. 7. 90 edges

Chapter Review, p. 397 1. about 196.9 m2 2. about 212.0 cm3 3. a) “Crash” b) “Crash” NEL

4. about 96.2 mL 5. e.g., radius 4.9 cm, height 10.0 cm 2 cm 6. e.g.,

b) }1}

c) 50

4. a)

b)

c) }1}

100 1 }} 6

2 1 }} 3

3

5. 70% 6. a) The event will happen for certain. b) It is impossible for the event to happen. 7. The bar for 30 to 39 would drop to 14, and the bar for 40 to 49 would increase to 15.

5 cm 5 cm 8 cm

6 cm

3. a) }57}

12.2 Theoretical and Experimental Probabilities, pp. 406–407 3. a) }1}

b) }1}

6

7. Since having six or more equilateral triangles meeting at a vertex would result in an interior angle of 360º or greater, the shape would be flat or turned upward. Since a Platonic solid must be a polyhedron, six or more equilateral triangles cannot meet at a vertex. 9. a) 5 faces b) e.g.,

c) }1}

2

4. a) 7, 8, 9, and 10

b)

5. a) }1}

c) }1}

e)

d)

f)

b)

2 1 }} 5

2 1 }} 2

7. a) P(greater than 8) 8. a)

3 }} 8

3 1 }} 10 3 }} 5 4 }} 13

g) }3} 4

b) P(9)

b) 0

c) 1

10. a) blue }1}, red }1}, green }1} 11. a) i)

2 1 }} 10

3

6

ii)

1 }} 2

iii) }1} 5

b) 250, 37 or 38

10. 10 edges 11. 6 vertices

12. b) box A }3}, box B }2}, box C }5}

Chapter 12, p. 399

c) Box A 13. e.g., rolling a die and not getting 6 14. No, because each outcome is not equally likely.

Getting Started, p. 401

12.3 Calculating Probabilities, p. 410

8

1. a) 3

c) increasing

b) trials 6 to 10 and 21 to 25 2. Event

NEL

Fraction form of probability

4

1 }} 13

number card greater than 5

5 }} 13

red

1 }} 2

d) }1} 6

Decimal Percent form of form of probability probability

0.077

7.7%

5

12

5. a) }1}

b) }1}

c) }2}

7. b)

c)

d) }1}

9. }1}

2 3 }} 8

2 1 }} 2

3 8

8

10. b) }7} 8

c) }7} 16

11. It is more likely that both Anthony and Peter will receive ribbons. 12. a) }1}

0.385

38.5%

9

b) 4 and 1, 1 and 4, 2 and 3, 3 and 2 c) }1} 2

0.5

50%

13. }7} 18

Answers 503