Metric and imperial units, perimeter, area and volume – Year 5 maths worksheet answers to download as PDF

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1. Answer to Question 1

   1. Bigger to smaller, multiply: 3.5 × 1,000 = 3,500 m.
   2. Smaller to bigger, divide: 450 ÷ 100 = 4.5 m.
   3. Multiply: 2.4 × 100 = 240 cm.
   4. Divide: 65 ÷ 10 = 6.5 cm.
   5. 3,200 ÷ 1,000 = 3.2 km.

2. Answer to Question 2

   1. There are 1,000 g in a kilogram, so divide by 1,000: 4,500 ÷ 1,000 = 4.5 kg.
   2. There are 1,000 ml in a litre, so multiply by 1,000: 2.4 × 1,000 = 2,400 ml.
   3. Millilitres to litres: divide by 1,000. 750 ÷ 1,000 = 0.75 l (three quarters of a litre).
   4. Kilograms to grams: multiply by 1,000. 0.35 × 1,000 = 350 g.
   5. 1.5 × 1,000 = 1,500 g, a kilogram and a half.

3. Answer to Question 3

   1. 10 × 2.5 = 25 cm.
   2. 3 × 30 = 90 cm.
   3. 40 ÷ 8 = 5, and 5 × 5 = 25 miles.
   4. 5 × 2.2 = 11 lb.
   5. 2 × 570 = 1,140 ml.

4. Answer to Question 4

   1. 2 × (9 + 4) = 2 × 13 = 26 cm.
   2. 4 × 7 = 28 cm.
   3. 2 × (15 + 6) = 2 × 21 = 42 m.
   4. Half of the perimeter is 15 cm, which is length + width. Width = 15 − 9 = 6 cm.

5. Answer to Question 5

   1. The area of a rectangle is length × width: 12 × 7 = 84 cm². It is the number of 1 cm squares that would cover it.
   2. 15 × 9 = 135 (10 × 9 = 90 and 5 × 9 = 45). The area is 135 m².
   3. A square is a rectangle with equal sides: 8 × 8 = 64 cm².
   4. Work backwards: length × width = 56, so width = 56 ÷ 8 = 7 cm. Check: 8 × 7 = 56.

6. Answer to Question 6

   1. Bottom layer: 4 × 3 = 12. Two layers: 12 × 2 = 24 cm³.
   2. Bottom layer: 5 × 2 = 10. Two layers: 20 cm³.
   3. Bottom layer: 3 × 3 = 9. Three layers: 9 × 3 = 27 cm³.
   4. 12 × 3 = 36 cm³.

7. Answer to Question 7

   1. 2 × (60 + 40) = 2 × 100 = 200 m.
   2. 1 km = 1,000 m. 1,000 ÷ 200 = 5 laps.
   3. 3 × 200 = 600 m = 0.6 km.
   4. 200 × 8 = £1,600.

8. Answer to Question 8

   1. Area = length × width = 5 × 4 = 20 m².
   2. Each square metre costs £12, so 20 × 12 = £240.
   3. The strip goes all the way round, so we need the perimeter: 5 + 4 + 5 + 4 = 2 × (5 + 4) = 18 m.
   4. Each length is 2 m: 18 ÷ 2 = 9 lengths, with nothing left over.

9. Answer to Question 9

   1. 1 pint ≈ 570 ml.
   2. 2.2 lb ≈ 1 kg and 2 kg ≈ 2 × 2.2 = 4.4 lb.
   3. 6 × 2.5 = 15 cm.
   4. 2 × 570 = 1,140 ml, which is more than 1 litre (1,000 ml) by 140 ml.

10. Answer to Question 10

    1. 12 × 8 = 96 m².
    2. 4 × 3 = 12 m².
    3. 96 − 12 = 84 m².
    4. 84 ÷ 20 = 4.2, so he needs 5 bags (4 bags are not enough).

11. Answer to Question 11

    1. The bottom layer is 10 cubes along and 5 cubes across: 10 × 5 = 50 cubes.
    2. The tank is 4 cm deep, so there are 4 layers of 50 cubes: 50 × 4 = 200 cm³.
    3. Each 1 cm³ holds 1 ml, so the tank holds 200 ml.
    4. There are 1,000 ml in a litre: 200 ÷ 1,000 = 0.2 litres (one fifth of a litre).

12. Answer to Question 12

    1. 64 ÷ 8 = 8, and 8 × 5 = 40 miles.
    2. The satnav gives about 40 miles, which is the same as the sign. Yes, they agree.
    3. 64 ÷ 12 = 5.33, so about 5 litres (a little more).
    4. 5 × £1.50 = £7.50 (about £8 with the extra).

13. Answer to Question 13

    1. 2 × (25 + 10) = 70 m.
    2. 25 × 10 = 250 m².
    3. 4 × 25 = 100 m. 1,000 − 100 = 900 m short.
    4. 70 × 6 = £420.

14. Answer to Question 14

    1. 2 × 1,000 = 2,000 g.
    2. 750 g = 0.75 kg. 2 + 0.75 + 1.5 = 4.25 kg.
    3. 1.5 × 2 = £3.
    4. 5 − 4.25 = 0.75 kg = 750 g.

15. Answer to Question 15

    1. 6 × 3 = 18 m².
    2. 2 × 1 = 2 m².
    3. 18 − 2 = 16 m².
    4. 16 ÷ 8 = 2 tins.
    5. 2 × £14 = £28.

16. Answer to Question 16

    1. 10 × 8 = 80 and 4 × 3 = 12, so 80 − 12 = 68 m².
    2. 10 + 3 + 4 + 5 + 6 + 8 = 36 m (same as the rectangle 2 × (10 + 8)).
    3. 36 × 9 = £324.
    4. 68 plants.
    5. 68 ÷ 2 = 34 m².

17. Answer to Question 17

    1. 6 × 4 = 24 cubes.
    2. 24 × 3 = 72 cubes.
    3. 72 × 2 = 144 g = 0.144 kg.
    4. 100 − 72 = 28 cubes.
    5. Second box: 5 × 5 × 4 = 100 cubes. 100 − 72 = 28. The second box holds 28 more cubes.

18. Answer to Question 18

    1. 2 × (8 + 4) = 2 × 12 = 24 m.
    2. 11 × 1 = 11 m²; 10 × 2 = 20 m²; 9 × 3 = 27 m²; 8 × 4 = 32 m²; 6 × 6 = 36 m².
    3. The 6 m by 6 m square has the greatest area, 36 m².
    4. The 11 m by 1 m pen has the smallest area, 11 m².
    5. The 11 m pen is the longest but has the smallest area (11 m²), while the 6 m pen is shorter but has the biggest area (36 m²). So he is wrong.

19. Answer to Question 19

    1. 3.5 l = 3,500 ml; 1,250 ml; 0.75 l = 750 ml.
    2. 3,500 + 1,250 + 750 = 5,500 ml = 5.5 litres.
    3. 5,500 ÷ 250 = 22 cups.
    4. 30 × 250 = 7,500 ml. 7,500 − 5,500 = 2,000 ml = 2 litres more.
    5. 2 pints ≈ 1,140 ml, which is much less than 5,500 ml. No, she is not right.

20. Answer to Question 20

    1. 2 × 1,000 = 2,000 cm³.
    2. 20 × 10 = 200 cm².
    3. Each 1 cm layer of water has a volume of 200 cm³. 2,000 ÷ 200 = 10 cm deep.
    4. The rise of 1 cm over the base is a layer of 200 cm³. So the stone has a volume of 200 cm³.