[PDF] Measurement – Workbook 7 Part 2

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Measurement - Workbook 7, Part 2

Worksheet ME7-22

page 42

1. a) 45 = 20 44 = 16

b) 20 16 c) 3 3 d) 203 =

60 163 =

48

2. a) lw

b) h c) lwh d) length width height

3. In a volume the length is

multiplied together three times.

4. a) Width: 2

Length: 2

Height: 2

Volume = 8

b) Width: 2 m

Length: 3 m

Height: 2 m

Volume = 12 m

3 c) Width: 2 cm

Length: 4 cm

Height: 2 cm

Volume = 16 cm

3 d) Width: 2 m

Length: 3 m

Height: 2 m

Volume = 12 m

3

Worksheet ME7-23

page 43

1. a) i) Hexagonal prism

ii) Pentagonal prism iii) Triangular prism b) Rectangles c) i) 6 ii) 5 iii) 3

2. a) Right prisms: B,F,A

Skew prisms: D, G

Not prisms: C,E

b) E: opposite bases not connected by parallel lines, C: bases are not congruent polygons 3. 4.

5. Teacher to check

6.

7. a) C: 5m, 3m, 7m

A: 3 cm, 3 cm, 4 cm

B: 2 km, 4 km, 4 km

b) Volume A: 36 cm 3

Volume B: 32 km

3

Volume C: 105 m

3

8. Answers will vary. Teacher

to check.

Worksheet ME7-24

page 46

1. a) 1/2

b) 4 c) 2

2. a) 1/2

b) 2 c) i) Volume of r.p. = 8

Volume of t.p. = 4

ii) Volume of r.p. = 70

Volume of t.p. = 35

iii) Volume of r.p. = 40

Volume of t.p. = 20

3. a) i) 1

ii) 5 iii) 4 b) i) 14 = 4 (note the typo: the area of the base is 1, not 2 as printed in the workbook) ii) 57 = 35 iii) 45 = 20 c) The numbers are the same.

4. Fraction of smaller

rectangles: 1/2

Fraction of whole

rectangle: 1/2

5. 1/2

6. a)

Fraction shaded: 1/2

Volume of r.p. = 16

Volume of t.p. = 8

b)

Fraction shaded: 1/2

Volume of r.p. = 54

Volume ot t.p. = 27

c)

Fraction shaded: 1/2

Volume of r.p. = 27

Volume ot t.p. = 13.5

d)

Fraction shaded: 1/2

Volume of r.p. = 160

Volume ot t.p. = 80

e)

Fraction shaded: 1/2

Volume of r.p. = 36

Volume ot t.p. = 18

f)

Fraction shaded: 1/2

Volume of r.p. = 450

Volume ot t.p. = 225

Worksheet ME7-25

page 48

Investigation 1

A. i) 6 cm

2 ii) 12 cm 2 iii) 8 cm 2 iv) 12 cm 2

B. i) 6 cm

3 ii) 12 cm 3 iii) 8 cm 3 iv) 12 cm 3

C. The numbers are all the

same, only the units differ.

D. i) 1 cm

ii) 2 cm iii) 2 cm iv) 3 cm

E. i) 6 cm

3 ii) 24 cm 3 iii) 16 cm 3 iv) 36 cm 3

F. The number of layers.

G. Volume of a rectangular

prism = (Area of the base) height

Investigation 2

A. i) 12

ii) 11 iii) 7

B. i) 12

ii) 11 iii) 7

C. i) 24

ii) 55 iii) 21

D. Yes, they are all made up

of two congruent polygons (the bases), connected by parallel lines.

E. Yes.

1. Volume of a right prism =

(Area of the base) × height a) Volume = 9;

Area of base = 3;

(Area of base) height =

33 = 9

b) Volume = 12;

Area of base = 4;

(Area of base) height =

43 = 12

2. a) 30

b) 72 c) 180

3. a) Triangle

b) Volume = (1/2)(lwh) = (lw2)h = (Area of base)height.

4. a) The volume of the

triangular part is 15h cm 3 and the volume of the rectangular part is 20h cm 3 , so the total volume is

15h + 20h cm

3 b) Yes. c) The area of the base is (15 + 20), so the volume is

15h + 20h = (15 + 20)h

= (Area of base) h.

5. a) 425 cm

3 b) 336 cm 3 c) 1125.3 cm 3

6. Answers may vary.

Teacher to check.

7. a) 1000 mL

Measurement - Workbook 7, Part 2 (continued)

2 b) 1000 cm 3

8. a) Volume = 1 000 cm

3

Capacity = 1 000

mL b) Volume = 10 000 cm 3

Capacity = 10 000

mL c) Volume = 1 000 000 cm 3

Capacity = 1 000

000 mL

9. a) 425 mL

b) 336 mL c) 1125.3 mL

10. 1890 cm

3

11. 20 cm

2 ; Volume = (Area of base) h so (Area of base) = Volume h.

12. 80 cm

2

BONUS: 7.4 cm

Worksheet ME7-26

page 51 1. a) b) c) d)

2. a) 1 cm

b) 3 cm c) 5 cm 3. a) b) front: 3 cm 2 top: 6 cm 2 right side: 2 cm 2 back: 3 cm 2 bottom: 6 cm 2 left side: 2 cm 2 c) 22 cm 2 4. a) b) c)

5. a) Back: 6 cm

2

Bottom: 12 cm

2

Left: 8 cm

2 b) Back: 15 cm 2

Bottom: 6 cm

2

Left: 10 cm

2 c) Back: 6 m 2

Bottom: 18 m

2

Left: 12 m

2 d) No, he has only counted half the faces. The surface area is 52 cm 2

6. a) i) front + back = 12

cm 2 top + bottom = 152 = 30 cm 2 right + left = 102 = 20 cm 2 ii) front + back = 18 cm 2 top + bottom = 24 cm 2 right + left = 24 cm 2 b) i) 62 cm 2 ii) 66 cm 2

7. a) Yes, since two of the

dimensions are the same. b) 224 cm 2

Worksheet ME7-27

page 53

1. a) Rectangular prism

b) Triangular prism c) Rectangular prism 2. # sides on base 3 4 5 6 # rectangular faces 3 4 5 6

The number of sides on the base

is the same as the number of rectangular faces.

3. a) 6

2 b) 2 1 1

4. a) First and second

nets. b) Second net c) Part a): third net has two bases on the same side.

Part b): first net has

one rectangular side too short, third net has the bases oriented in opposite ways 5. a) b) 6. a) b) c) 7. a) b) c) d) 8. b)

9. a) back: 23 = 6 cm

2 right face: 2 cm 2 left face: 2 cm 2 top: 3 cm 2 bottom: 3 cm 2 surface area: 20 cm 2 b) front: 4 cm 2 back: 4 cm 2 right face: 2 cm 2 left face: 2 cm 2 top: 8 cm 2 bottom: 8 cm 2 surface area: 28 cm 2

10. a) surface area: 42

cm 2 volume: 18 cm 3 b) surface area: 28 cm 2 volume: 8 cm 3 c) surface area: 62 cm 2 volume: 30 cm 3

11. a)

b) top: 12 cm 2 bottom: 12 cm 2 front: 3 cm 2 back: 3 cm 2 right: 4 cm 2 left: 4 cm 2 c) 38 cm 2

12. a)

b) 60 m 2 c) 24 m 3

Worksheet ME7-28

page 56

1. a) 94 cm

2 b) 40 cm 2 c) 52 cm 2

2. Multiply by 2 since this will

account for the back, bottom, and left faces.

3. (area of top + area of right

side + area of front) 2, (area of bottom + area of left side + area of front) 2, (area of top + area of left side + area of back) 2

4. a) 4 m

b) 3 m c) 7 m

5. a) 5 m

b) 5 m c) 4 m

6. a = 6 m, b = 3 m, c = 2 m

7. Calculate the area of each

face and add them all together.

Calculate the area of the

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