Measurement concepts for the 11+ exam
**Length, Mass, Capacity, Perimeter, Area, and Volume.**
#### **1. Units of Measurement (Length, Mass, Capacity)**
* **Length:** Millimetre (mm), Centimetre (cm), Metre (m), Kilometre (km).
* **Conversion:** 1 cm = 10 mm, 1 m = 100 cm, 1 km = 1000 m.
* **Mass (Weight):** Milligram (mg), Gram (g), Kilogram (kg), Tonne (t).
* **Conversion:** 1 g = 1000 mg, 1 kg = 1000 g, 1 t = 1000 kg.
* **Capacity (Volume of liquids):** Millilitre (ml), Centilitre (cl), Litre (l).
* **Conversion:** 1 cl = 10 ml, 1 l = 100 cl, 1 l = 1000 ml.
**Key Skill: Conversion**
To convert from a larger unit to a smaller unit, **multiply**.
To convert from a smaller unit to a larger unit, **divide**.
*Example:*
* Convert 2.5m to cm: 2.5 × 100 = **250 cm**
* Convert 450ml to litres: 450 ÷ 1000 = **0.45 litres**
---
#### **2. Perimeter**
The perimeter is the total distance around the outside of a 2D shape. You find it by adding up the lengths of all the sides.
* **Rectangle:** Perimeter = 2 × (Length + Width)
* **Square:** Perimeter = 4 × Side Length
* **Irregular Shapes:** Add every side together. Look carefully for any missing lengths that need to be calculated.
*Example: Find the perimeter of a rectangle with length 8cm and width 5cm.*
* Perimeter = 2 × (8cm + 5cm) = 2 × 13cm = **26cm**
#### **3. Area**
Area is the amount of space inside a 2D shape. It is measured in square units (e.g., cm², m²).
* **Rectangle:** Area = Length × Width
* **Square:** Area = Side × Side = Side²
* **Triangle:** Area = (Base × Height) ÷ 2
* **Compound Shapes:** Split the shape into rectangles (or other known shapes), find the area of each part, and then add them together.
*Example: Find the area of a triangle with a base of 10cm and a height of 6cm.*
* Area = (10cm × 6cm) ÷ 2 = 60cm² ÷ 2 = **30cm²**
#### **4. Volume**
Volume is the amount of space a 3D object takes up. It is measured in cubic units (e.g., cm³, m³). For regular 3D shapes like cuboids, it's straightforward.
* **Cuboid (Rectangular Prism):** Volume = Length × Width × Height
*Example: Find the volume of a box that is 5cm long, 4cm wide, and 3cm high.*
* Volume = 5cm × 4cm × 3cm = **60cm³**
### **Practice Questions (Modelled on GL Assessment Style)**
#### **Section A: Units and Conversions (15 Questions)**
1. Convert 3.2 kilometres into metres.
2. How many millilitres are there in 4.5 litres?
3. A bag of flour weighs 1.5kg. What is its weight in grams?
4. Convert 2560 centimetres to metres.
5. A bottle contains 0.8 litres of water. How many centilitres is this?
6. If a pencil is 17cm long, how long is it in millimetres?
7. Add 250g and 1.2kg, giving your answer in grams.
8. Subtract 450ml from 2 litres, giving your answer in millilitres.
9. How many 200ml glasses can be completely filled from a 1.5-litre jug?
10. A piece of string is 4m long. A 75cm piece is cut off. How many centimetres of string are left?
11. Convert 12.5cm into millimetres.
12. A baby weighs 4.2kg. What is its weight in grams?
13. A petrol tank holds 60 litres. How many centilitres is this?
14. Which is heavier: 0.45kg or 480g? Show your working.
15. A swimming pool is 25m long. How many lengths make up 1 kilometre?
#### **Section B: Perimeter (10 Questions)**
16. A rectangle is 12cm long and 7cm wide. What is its perimeter?
17. A square has a side length of 9cm. Calculate its perimeter.
18. An equilateral triangle has a side length of 15cm. Find its perimeter.
19. Find the perimeter of a regular hexagon with a side length of 6.5cm.
20. Calculate the perimeter of this shape (all angles are right angles):
```
┌─────┐
│ │ Height: 8cm
│ │ Width: 10cm
└─────┘ (A simple rectangle)
```
21. A rectangular garden has a perimeter of 40m. If its length is 12m, what is its width?
22. Find the perimeter of this L-shaped figure:
```
┌───┐
│ A │┌───┐
│ ││ B │
└───┘└───┘
```
* Section A is a 6cm by 4cm rectangle.
* Section B is a 3cm by 4cm rectangle attached to the right of A.
23. The perimeter of a square is 52cm. What is the length of one side?
24. A triangle has sides of length 8cm, 8cm, and 5cm. What is its perimeter?
25. Fencing costs £15 per metre. How much would it cost to fence a square field with sides of 20m?
#### **Section C: Area (15 Questions)**
26. What is the area of a rectangle measuring 9cm by 6cm?
27. A square has sides of 7cm. What is its area?
28. Find the area of a triangle with a base of 10cm and a height of 8cm.
29. A rectangular room is 5m long and 4m wide. What is the area of the floor?
30. A tile is a square with 25cm sides. What is its area in cm²?
31. Find the area of this compound shape:
```
┌───────────┐
│ │
│ │ Height: 12cm
├─────┐ │ Total Width: 15cm
│ │ │ The smaller rectangle (cut out) is 5cm wide and 6cm high.
└─────┘ │
```
*(Hint: Find the area of the large rectangle and subtract the area of the small one.)*
32. The area of a square is 81cm². What is the length of one side?
33. The area of a rectangle is 54cm². If its length is 9cm, what is its width?
34. A triangular sail has a base of 4m and a height of 3m. What is its area?
35. A lawn is 10m long and 8m wide. What is its area?
36. A picture frame is 30cm by 20cm. What is the area of the picture it can hold?
37. A right-angled triangle has legs of 6cm and 8cm. What is its area?
38. A parallelogram has a base of 12cm and a vertical height of 5cm. What is its area? (Area of parallelogram = base × height)
39. A room is 6m long and 4.5m wide. What is the area of the room in m²?
40. Carpet costs £18 per square metre. How much does it cost to carpet a room that is 5m by 4m?
#### **Section D: Volume (10 Questions)**
41. What is the volume of a cuboid with length 5cm, width 3cm, and height 4cm?
42. A box has dimensions 10cm, 6cm, and 5cm. Calculate its volume.
43. A cube has a side length of 7cm. What is its volume?
44. The volume of a cuboid is 240cm³. If its length is 10cm and its width is 6cm, what is its height?
45. A storage container is 2m long, 1.5m wide, and 1m high. What is its volume in cubic metres?
46. How many cubes of side 1cm would fit into a box that is 10cm long, 5cm wide, and 2cm high?
47. A fish tank is 60cm long, 30cm wide, and 40cm high. What is its volume in cm³?
48. Convert the volume from question 47 into litres. (Remember: 1000cm³ = 1 litre)
49. A book has a volume of 600cm³. It is 20cm long and 5cm wide. How thick is the book?
50. A brick has a volume of 1500cm³. Its length is 25cm and its width is 10cm. What is its height?
1. **(Conversion)** John needs 2.5 metres of ribbon. The shop sells it by the centimetre. How many centimetres does he need to buy?
* **A.** 25 cm
* **B.** 205 cm
* **C.** 250 cm
* **D.** 2500 cm
2. **(Perimeter)** A rectangular playground is 40 metres long and has a perimeter of 120 metres. How wide is it?
* **A.** 20 m
* **B.** 30 m
* **C.** 40 m
* **D.** 80 m
3. **(Area)** The area of a square carpet is 36m². What is the length of one of its sides?
* **A.** 4 m
* **B.** 6 m
* **C.** 9 m
* **D.** 12 m
4. **(Volume)** A cardboard box is 20cm long, 15cm wide and 10cm high. What is its volume?
* **A.** 45 cm³
* **B.** 300 cm³
* **C.** 3000 cm³
* **D.** 30000 cm³
5. **(Compound Area)** What is the area of the shaded "L" shape?
```
┌───────────┐ 10cm
│ │
│ ┌──────┤ 6cm
│ │ Shad │
└────┴──────┘
4cm 6cm
```
* **A.** 60 cm²
* **B.** 76 cm²
* **C.** 84 cm²
* **D.** 100 cm²
6. **(Capacity)** A jug contains 1.8 litres of lemonade. How many 150ml glasses can be completely filled from the jug?
* **A.** 8
* **B.** 12
* **C.** 15
* **D.** 18
7. **(Mass)** A parcel weighs 2.4kg. The postage cost is £3.50 for the first kilogram and £1.20 for each additional 500g or part thereof. How much does it cost to post the parcel?
* **A.** £4.70
* **B.** £5.90
* **C.** £6.10
* **D.** £7.90
8. **(Perimeter/Conversion)** Sam runs 5 times around a square field with sides of 120m. What is the total distance he runs in kilometres?
* **A.** 0.6 km
* **B.** 2.4 km
* **C.** 6 km
* **D.** 24 km
9. **(Volume in context)** A rectangular tank is 50cm long, 40cm wide and 30cm high. It is filled with water to a depth of 20cm. What is the volume of water in the tank in litres?
* **A.** 24 litres
* **B.** 40 litres
* **C.** 60 litres
* **D.** 40000 litres
10. **(Reverse Area)** The area of a rectangle is 84cm². Its length is 12cm. What is its perimeter?
* **A.** 7 cm
* **B.** 38 cm
* **C.** 48 cm
* **D.** 96 cm
### **Answer Key & Solutions**
**Section A:**
1. 3200m
2. 4500ml
3. 1500g
4. 25.6m
5. 80cl
6. 170mm
7. 1450g (1.2kg = 1200g, 1200+250=1450g)
8. 1550ml (2 litres = 2000ml, 2000-450=1550ml)
9. 7 glasses (1.5l = 1500ml, 1500 ÷ 200 = 7.5, so 7 full glasses)
10. 325cm (4m = 400cm, 400-75=325cm)
11. 125mm
12. 4200g
13. 6000cl
14. 480g (0.45kg = 450g, so 480g is heavier)
15. 40 lengths (1km = 1000m, 1000 ÷ 25 = 40)
**Section B:**
16. 38cm (2x(12+7)=38)
17. 36cm (4x9=36)
18. 45cm (3x15=45)
19. 39cm (6x6.5=39)
20. 36cm (2x(10+8)=36)
21. 8m (Perimeter = 2L + 2W, 40=2(12)+2W, 40=24+2W, 16=2W, W=8)
22. 26cm (The outer edges are 6cm, 4cm, 3cm, 3cm, 4cm, 6cm. 6+4+3+3+4+6=26)
23. 13cm (52 ÷ 4 = 13)
24. 21cm (8+8+5=21)
25. £1200 (Perimeter = 4x20=80m, Cost = 80x15=£1200)
**Section C:**
26. 54cm² (9x6=54)
27. 49cm² (7x7=49)
28. 40cm² ((10x8)/2=40)
29. 20m² (5x4=20)
30. 625cm² (25x25=625)
31. 150cm² (Area large = 15x12=180, Area small = 5x6=30, 180-30=150)
32. 9cm (√81=9)
33. 6cm (54 ÷ 9 = 6)
34. 6m² ((4x3)/2=6)
35. 80m² (10x8=80)
36. 600cm² (30x20=600)
37. 24cm² ((6x8)/2=24)
38. 60cm² (12x5=60)
39. 27m² (6x4.5=27)
40. £360 (Area=5x4=20m², Cost=20x18=£360)
**Section D:**
41. 60cm³ (5x3x4=60)
42. 300cm³ (10x6x5=300)
43. 343cm³ (7x7x7=343)
44. 4cm (Volume = LxWxH, 240=10x6xH, 240=60xH, H=4)
45. 3m³ (2x1.5x1=3)
46. 100 cubes (Volume of box = 10x5x2=100cm³. 100 cubes of 1cm³ each.)
47. 72000cm³ (60x30x40=72000)
48. 72 litres (72000 ÷ 1000 = 72)
49. 6cm (Volume = LxWxH, 600=20x5xH, 600=100xH, H=6)
50. 6cm (Volume = LxWxH, 1500=25x10xH, 1500=250xH, H=6)
**GL Style Questions:**
1. **C.** 2.5m × 100 = 250 cm
2. **A.** Perimeter = 2(L+W). 120 = 2(40+W) -> 120=80+2W -> 40=2W -> W=20m
3. **B.** Area of square = side². 36 = side². Side = 6m.
4. **C.** Volume = 20 × 15 × 10 = 3000 cm³
5. **B.** Method 1: Area of whole rectangle (10x10=100) minus area of missing square (4x6=24) -> 100-24=76cm². Method 2: Area of vertical rectangle (10x4=40) + area of horizontal rectangle (6x6=36) -> 40+36=76cm².
6. **B.** 1.8 litres = 1800ml. 1800 ÷ 150 = 12.
7. **C.** 2.4kg. First kg = £3.50. Remaining weight: 1.4kg. This counts as three 500g portions (500g, 1000g, 1500g). 3 x £1.20 = £3.60. Total = £3.50 + £3.60 = £7.10. *(Note: "part thereof" means you round up the remaining weight to the next 500g. 1.4kg is rounded up to 1.5kg for charging purposes, which is three 500g units)*. **Correction: The calculation should be: First kg = £3.50. The remaining 1.4kg requires counting 500g units. 1.4kg = 1400g. 1400g / 500g = 2.8, which rounds up to 3 units. 3 x £1.20 = £3.60. Total = £3.50 + £3.60 = £7.10.**
8. **B.** Perimeter of field = 4 x 120m = 480m. Distance run = 5 x 480m = 2400m. 2400m = 2.4 km.
9. **B.** The water forms a cuboid: Length=50cm, Width=40cm, Height=20cm. Volume of water = 50x40x20 = 40000 cm³. 40000 cm³ = 40 litres.
10. **B.** Area = L x W. 84 = 12 x W. So W = 7cm. Perimeter = 2(L+W) = 2(12+7) = 2(19) = 38cm.
Of course. Here is a substantial additional set of practice questions, structured to provide extensive preparation for the Measurement section of the 11+ exam in the style of GL Assessment.
### **Additional Practice Questions (GL Assessment Style)**
#### **Set 1: Units of Measurement (10 Questions)**
1. Which unit would be most appropriate to measure the weight of a new-born baby?
a) grams
b) kilograms
c) millilitres
d) centimetres
2. Which unit would be most appropriate to measure the capacity of a teaspoon?
a) litres
b) millilitres
c) grams
d) centimetres
3. Which unit would be most appropriate to measure the length of a football pitch?
a) millimetres
b) centimetres
c) metres
d) kilometres
4. The length of a book is best measured in:
a) kilometres
b) metres
c) centimetres
d) milligrams
5. The amount of water in a full bathtub is best measured in:
a) millilitres
b) centilitres
c) litres
d) kilograms
6. The weight of a paperclip is best measured in:
a) kilograms
b) grams
c) milligrams
d) litres
7. Which of the following is a measure of volume?
a) metre
b) gram
c) litre
d) degree
8. Which of the following is a measure of mass?
a) litre
b) metre
c) kilogram
d) kilometre
9. The height of a tree is best measured in:
a) mm
b) cm
c) m
d) km
10. The weight of a family car is best measured in:
a) grams
b) kilograms
c) tonnes
d) litres
#### **Set 2: Units and Conversions (10 Questions)**
11. Convert 4.7 kilometres into metres.
12. How many grams are there in 3.05 kilograms?
13. A bottle holds 2.25 litres of juice. How many millilitres is this?
14. Convert 185 centimetres into metres.
15. A piece of string is 2.4 metres long. How long is it in centimetres?
16. Add 1.2 kg and 850 g, giving your answer in grams.
17. Subtract 325 ml from 1.5 litres, giving your answer in millilitres.
18. How many 250 ml cups can be completely filled from a 3-litre bottle?
19. A baby was 52 cm long at birth. How many millimetres is this?
20. A bag of potatoes weighs 5 kg. I use 1200 g for a meal. How many grams of potatoes are left?
#### **Set 3: Perimeter (10 Questions)**
21. A rectangle has a length of 15 cm and a width of 9 cm. What is its perimeter?
22. A regular pentagon has a side length of 8 cm. Calculate its perimeter.
23. An isosceles triangle has two sides of 12 cm and a base of 7 cm. Find its perimeter.
24. Calculate the perimeter of a square with a side length of 6.2 cm.
25. A rectangular garden has a perimeter of 50 m. If its width is 10 m, what is its length?
26. Find the perimeter of this shape (all angles are right angles):
```
┌──────┐
│ │─────┐
│ │ │
└──────┘ │
└─────┘
```
* The overall shape is like a capital 'L'. The long vertical side is 12 cm, the long horizontal side is 15 cm, the width of the 'L' arm is 4 cm, and the height of the 'L' arm is 5 cm.
*(Hint: The perimeter is the same as that of a 15 cm by 12 cm rectangle.)*
27. The perimeter of a regular octagon is 96 cm. What is the length of one side?
28. Fencing costs £24 per metre. How much would it cost to fence a rectangular garden that is 18 m long and 12 m wide?
29. A square has a perimeter of 44 cm. What is the length of one side?
30. Find the perimeter of a triangle with sides of 12.5 cm, 8.7 cm, and 10.3 cm.
#### **Set 4: Area (10 Questions)**
31. What is the area of a rectangle measuring 11 cm by 8 cm?
32. A square has sides of 9.5 cm. What is its area?
33. Find the area of a triangle with a base of 12 cm and a height of 9 cm.
34. A rectangular field is 120 m long and 80 m wide. What is its area in square metres?
35. The area of a square is 144 cm². What is the length of one side?
36. The area of a rectangle is 96 cm². If its width is 8 cm, what is its length?
37. Find the area of this compound shape:
```
┌─────────────┐ 8m
│ │
│ │
├──────┐ │ 4m
│ │ │
│ │ │
└──────┴──────┘
5m 7m
```
*(Hint: Split into two rectangles: 8m x 7m and 4m x 5m)*
38. A parallelogram has a base of 10 cm and a vertical height of 6 cm. What is its area?
39. A right-angled triangle has legs of 5 cm and 12 cm. What is its area?
40. Floor tiles are 25 cm squares. What is the area of one tile in cm²?
#### **Set 5: Volume (10 Questions)**
41. What is the volume of a cuboid with length 8 cm, width 5 cm, and height 3 cm?
42. A cube has a side length of 6 cm. What is its volume?
43. The volume of a box is 600 cm³. If its length is 15 cm and its width is 5 cm, what is its height?
44. A storage crate is 3 m long, 2 m wide, and 1.5 m high. What is its volume in m³?
45. How many 1 cm cubes are needed to make a larger cube with sides of 5 cm?
46. A fish tank is 80 cm long, 35 cm wide, and 40 cm high. What is its volume in cm³?
47. Convert the volume from question 46 into litres.
48. A book is 4 cm thick, 20 cm long, and 15 cm wide. What is its volume?
49. A brick has a volume of 1200 cm³. Its length is 20 cm and its height is 5 cm. What is its width?
50. A rectangular pond is 4 m long, 2 m wide, and is filled with water to a depth of 0.8 m. What is the volume of water in the pond in cubic metres?
---
### **Fictional "Previous Year Paper" Section (50 Questions)**
**Instructions:** Answer all questions. Show your working if necessary.
51. 2.5 km = __________ m
52. 3450 g = __________ kg
53. 7250 ml = __________ l
54. A ruler is 30 cm long. How many mm is this? __________
55. To measure the weight of an apple, you would use: (kg/g/mg)
56. To measure the amount of medicine in a spoon, you would use: (l/cl/ml)
57. The perimeter of a square with 13 cm sides is __________ cm.
58. The area of a 9 cm by 6 cm rectangle is __________ cm².
59. The volume of a 7 cm cube is __________ cm³.
60. A triangle has a base of 10 cm and an area of 35 cm². Its height is __________ cm.
61. **Multiple Choice:** Which of these is the longest?
a) 1.2 m
b) 125 cm
c) 1100 mm
d) 0.012 km
62. **Multiple Choice:** Which of these is the heaviest?
a) 1.05 kg
b) 1055 g
c) 150,000 mg
d) 10,500 cg
63. **Multiple Choice:** The perimeter of the shape below is:
```
┌─────────┐ 5cm
│ │
│ │ 3cm
└─────────┘
```
a) 8 cm
b) 15 cm
c) 16 cm
d) 30 cm
64. **Multiple Choice:** The area of the shape in question 63 is:
a) 8 cm²
b) 15 cm²
c) 16 cm²
d) 30 cm²
65. **Multiple Choice:** A cuboid has a volume of 120 ml. This is the same as:
a) 120 cm³
b) 120 l
c) 120 m³
d) 12 cm³
66. Calculate the perimeter of a regular hexagon with side length 7.5 cm. __________
67. A roll of tape is 5 m long. I use 3 pieces of 85 cm each. How many cm of tape are left? __________
68. A rectangle has an area of 72 m² and a length of 9 m. Its perimeter is __________ m.
69. A swimming pool is 25 m long, 10 m wide, and 2 m deep. Its volume is __________ m³.
70. How many 50 cl bottles can be filled from a 20 litre container? __________
71. 0.8 m + 45 cm + 220 mm = __________ cm
72. 3 kg - 450 g = __________ g
73. 4.5 l ÷ 150 ml = __________
74. A square plot of land has a perimeter of 200 m. What is its area? __________ m²
75. A recipe needs 500 g of flour. If I triple the recipe, how many kilograms of flour do I need? __________ kg
76. **Word Problem:** Sarah is framing a picture that is 18 cm by 24 cm. The frame is 3 cm wide all the way around. What is the perimeter of the outside of the frame?
a) 84 cm
b) 96 cm
c) 108 cm
d) 120 cm
77. **Word Problem:** A box of chocolates weighs 1.2 kg. The empty box weighs 150 g. What is the weight of the chocolates in grams?
a) 1050 g
b) 1150 g
c) 1200 g
d) 1350 g
78. **Word Problem:** A rectangular tank 60 cm long and 40 cm wide contains 72 litres of water. How deep is the water?
a) 3 cm
b) 30 cm
c) 33 cm
d) 300 cm
79. **Word Problem:** Tiles are 20 cm squares. How many tiles are needed to cover a rectangular floor that is 4 m long and 3 m wide?
a) 300
b) 400
c) 500
d) 600
80. **Word Problem:** A car uses 1 litre of petrol to travel 12 km. How many litres are needed to travel 150 km?
a) 10.5 l
b) 12.5 l
c) 13.5 l
d) 14.5 l
81. - 100. *(Continue with similar style questions focusing on multi-step problems, compound shapes, and real-life contexts for the remaining 20 questions. The pattern is well established for practice.)*
---
### **Answer Key & Solutions**
**Set 1:**
1. b) kilograms
2. b) millilitres
3. c) metres
4. c) centimetres
5. c) litres
6. b) grams
7. c) litre
8. c) kilogram
9. c) m
10. c) tonnes
**Set 2:**
11. 4700 m
12. 3050 g
13. 2250 ml
14. 1.85 m
15. 240 cm
16. 2050 g (1200g + 850g)
17. 1175 ml (1500ml - 325ml)
18. 12 cups (3000ml / 250ml = 12)
19. 520 mm
20. 3800 g (5000g - 1200g)
**Set 3:**
21. 48 cm (2x(15+9))
22. 40 cm (5x8)
23. 31 cm (12+12+7)
24. 24.8 cm (4x6.2)
25. 15 m (50 = 2(L+10) -> 50=2L+20 -> 30=2L -> L=15)
26. 54 cm (2x(15+12))
27. 12 cm (96 / 8)
28. £1440 (Perimeter=2x(18+12)=60m. Cost=60x24=£1440)
29. 11 cm (44 / 4)
30. 31.5 cm (12.5+8.7+10.3)
**Set 4:**
31. 88 cm²
32. 90.25 cm² (9.5x9.5)
33. 54 cm² ((12x9)/2)
34. 9600 m²
35. 12 cm (√144)
36. 12 cm (96 / 8)
37. 76 m² (Area1=8x7=56, Area2=4x5=20, Total=76)
38. 60 cm²
39. 30 cm² ((5x12)/2)
40. 625 cm²
**Set 5:**
41. 120 cm³
42. 216 cm³
43. 8 cm (600 = 15x5xH -> 600=75H -> H=8)
44. 9 m³
45. 125 cubes (5x5x5)
46. 112,000 cm³ (80x35x40)
47. 112 litres (112,000 / 1000)
48. 1200 cm³ (4x20x15)
49. 12 cm (1200 = 20x5xW -> 1200=100W -> W=12)
50. 6.4 m³ (4x2x0.8)
**Fictional Paper (Selected Answers):**
51. 2500
52. 3.45
53. 7.25
54. 300
55. g
56. ml
57. 52
58. 54
59. 343
60. 7 (35 = (10xh)/2 -> 35=5h -> h=7)
61. d) 0.012 km (which is 12 m)
62. b) 1055 g (1.055 kg, which is more than 1.05kg)
63. c) 16 cm (5+3+5+3) *Correction: The shape shown is a rectangle 5cm by 3cm. Perimeter = 2x(5+3)=16cm.*
64. b) 15 cm² (5x3)
65. a) 120 cm³ (1 ml = 1 cm³)
66. 45 cm (6x7.5)
67. 245 cm (500 cm - (3x85 cm) = 500-255=245)
68. 34 m (Width=72/9=8m, Perimeter=2x(9+8)=34m)
69. 500 m³ (25x10x2)
70. 40 bottles (20 l = 200 cl, 200/50=40)
71. 147 cm (80cm + 45cm + 22cm)
72. 2550 g (3000g - 450g)
73. 30 (4500ml / 150ml = 30)
74. 2500 m² (Side=200/4=50m, Area=50x50=2500)
75. 1.5 kg (500g x 3 = 1500g = 1.5kg)
76. c) 108 cm (Frame outer dimensions: 18+6=24cm, 24+6=30cm. Perimeter=2x(24+30)=108cm)
77. a) 1050 g (1200g - 150g)
78. b) 30 cm (Volume of water=72,000 cm³. Depth = 72,000 / (60x40) = 72,000/2400 = 30cm)
79. a) 300 (Floor area=4x3=12 m²=120,000 cm². Tile area=20x20=400 cm². Number of tiles=120,000/400=300)
80. b) 12.5 l (150 / 12 = 12.5)
### **Additional Practice Questions (81-100): Multi-step, Compound Shapes & Real-Life Contexts**
Here are 20 more challenging questions that require multiple steps, involve compound shapes, and are set in real-life contexts, following the GL Assessment style.
---
**81. Multi-step (Perimeter & Conversion):** A rectangular garden is 15 metres long and 10 metres wide. A path of width 1 metre is built around the garden inside the boundary. What is the perimeter of the inner rectangle (the garden excluding the path)?
**82. Compound Shapes (Area):** Find the area of the shaded region in the following figure:
```
┌─────────────┐ 12 cm
│ │
│ ┌─────┐ │
│ │ │ │ 8 cm
│ └─────┘ │
└─────────────┘
6 cm x 4 cm
```
(The inner rectangle is centered within the larger one)
**83. Real-life Context (Volume):** A water tank is in the shape of a cuboid. It is 2 m long, 1.5 m wide, and 1 m high. How many litres of water can it hold when full?
**84. Multi-step (Conversion & Addition):** A recipe requires 2.5 kg of flour, 500 g of sugar, and 250 g of butter. What is the total weight of the ingredients in grams?
**85. Compound Shapes (Perimeter):** Calculate the perimeter of this L-shape:
```
┌───────────┐
│ │
│ │───┐ 3 cm
│ │ │
└───────────┘ │
└───────┘
10 cm 4 cm
```
(Total height: 6 cm)
**86. Real-life Context (Capacity):** A jug contains 2.5 litres of lemonade. How many 150 ml glasses can be filled completely from the jug?
**87. Multi-step (Area & Cost):** A rectangular room is 5 m long and 4 m wide. The cost of carpeting is £15 per square metre. How much does it cost to carpet the room?
**88. Compound Shapes (Area):** A garden is in the shape of a rectangle with a semicircular patio attached to one of the shorter ends. The rectangle is 10 m long and 4 m wide. The semicircle has a diameter of 4 m. What is the total area of the garden? (Use Ο = 3.14)
**89. Multi-step (Volume & Conversion):** A rectangular tank is 50 cm long, 40 cm wide, and 30 cm high. It is filled with water to a depth of 20 cm. How many more litres of water are needed to fill the tank completely?
**90. Real-life Context (Mass):** A box of 12 identical packets of cereal weighs 4.8 kg. If the empty box weighs 300 g, what is the weight of one packet of cereal in grams?
**91. Multi-step (Perimeter & Ratio):** The length of a rectangle is twice its width. If the perimeter of the rectangle is 60 cm, what is its area?
**92. Compound Shapes (Volume):** A storage container is made by joining two cuboids. The first cuboid is 2 m long, 1.5 m wide, and 1 m high. The second cuboid is placed on top of the first and is 1 m long, 1.5 m wide, and 0.5 m high. What is the total volume of the container?
**93. Real-life Context (Time & Capacity):** A tap fills a bath at a rate of 15 litres per minute. The bath has a capacity of 180 litres. How long does it take to fill the bath in minutes?
**94. Multi-step (Area & Percentage):** A square field has an area of 10000 m². A path of width 10 m is built around the field. What is the area of the path?
**95. Compound Shapes (Perimeter):** A square frame is made by cutting out a smaller square of side 4 cm from the center of a larger square of side 10 cm. What is the perimeter of the frame?
**96. Real-life Context (Speed, Distance, Time):** A car travels at a constant speed of 80 km/h. How far does it travel in 45 minutes?
**97. Multi-step (Area & Multiplication):** A rectangular wall is 3 m high and 5 m wide. Each tile is a square of side 25 cm. How many tiles are needed to cover the wall?
**98. Compound Shapes (Volume):** A wooden block has a cuboid with dimensions 10 cm, 8 cm, and 5 cm. A hole in the shape of a cuboid of dimensions 4 cm, 3 cm, and 5 cm is drilled through the block. What is the volume of the remaining block?
**99. Real-life Context (Money & Mass):** Oranges cost £1.20 per kilogram. How much does 500 g of oranges cost?
**100. Multi-step (Volume & Capacity):** A swimming pool is 20 m long, 10 m wide, and 2 m deep. How many litres of water are needed to fill it completely?
---
### **Answer Key & Solutions (Questions 81-100)**
**81.** **42 m**
*Solution: Path is inside, so inner rectangle dimensions: Length = 15 - 2×1 = 13 m, Width = 10 - 2×1 = 8 m. Perimeter = 2×(13+8) = 42 m.*
**82.** **72 cm²**
*Solution: Area of outer rectangle = 12×8 = 96 cm². Area of inner rectangle = 6×4 = 24 cm². Shaded area = 96 - 24 = 72 cm².*
**83.** **3000 litres**
*Solution: Volume = 2×1.5×1 = 3 m³. Since 1 m³ = 1000 litres, capacity = 3×1000 = 3000 litres.*
**84.** **3250 g**
*Solution: 2.5 kg = 2500 g. Total = 2500 + 500 + 250 = 3250 g.*
**85.** **40 cm**
*Solution: The perimeter is the same as a 10 cm × 6 cm rectangle = 2×(10+6) = 32 cm, PLUS the two extra 4 cm segments = 32 + 8 = 40 cm. (Alternatively, sum all sides: 10+6+3+4+3+10+4 = 40 cm)*
**86.** **16 glasses**
*Solution: 2.5 litres = 2500 ml. 2500 ÷ 150 = 16.66... so 16 full glasses.*
**87.** **£300**
*Solution: Area = 5×4 = 20 m². Cost = 20×15 = £300.*
**88.** **46.28 m²**
*Solution: Rectangle area = 10×4 = 40 m². Semicircle area = (1/2)×Ο×r² = 0.5×3.14×2² = 6.28 m². Total = 40 + 6.28 = 46.28 m².*
**89.** **20 litres**
*Solution: Volume of tank = 50×40×30 = 60000 cm³. Volume of water = 50×40×20 = 40000 cm³. Volume needed = 60000 - 40000 = 20000 cm³ = 20 litres (since 1000 cm³ = 1 litre).*
**90.** **375 g**
*Solution: Total weight of packets = 4800 g - 300 g = 4500 g. Weight per packet = 4500 ÷ 12 = 375 g.*
**91.** **200 cm²**
*Solution: Let width = w, length = 2w. Perimeter = 2×(2w+w) = 6w = 60 cm, so w = 10 cm, length = 20 cm. Area = 10×20 = 200 cm².*
**92.** **3.75 m³**
*Solution: Volume of first cuboid = 2×1.5×1 = 3 m³. Volume of second = 1×1.5×0.5 = 0.75 m³. Total = 3.75 m³.*
**93.** **12 minutes**
*Solution: Time = 180 ÷ 15 = 12 minutes.*
**94.** **4400 m²**
*Solution: Side of field = √10000 = 100 m. Side with path = 100 + 10 + 10 = 120 m. Area with path = 120×120 = 14400 m². Path area = 14400 - 10000 = 4400 m².*
**95.** **56 cm**
*Solution: Outer perimeter = 4×10 = 40 cm. Inner perimeter = 4×4 = 16 cm. Total perimeter = 40 + 16 = 56 cm.*
**96.** **60 km**
*Solution: 45 minutes = 0.75 hours. Distance = 80 × 0.75 = 60 km.*
**97.** **240 tiles**
*Solution: Wall area = 3×5 = 15 m² = 150000 cm². Tile area = 25×25 = 625 cm². Number of tiles = 150000 ÷ 625 = 240.*
**98.** **340 cm³**
*Solution: Volume of large cuboid = 10×8×5 = 400 cm³. Volume of hole = 4×3×5 = 60 cm³. Remaining volume = 400 - 60 = 340 cm³.*
**99.** **£0.60**
*Solution: 500 g = 0.5 kg. Cost = 0.5 × 1.20 = £0.60.*
**100.** **400,000 litres**
*Solution: Volume = 20×10×2 = 400 m³. Since 1 m³ = 1000 litres, water needed = 400×1000 = 400,000 litres.*
