Converting units, area, perimeter and volume – Year 6 maths worksheet answers to download as PDF

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1. Answer to Question 1

   1. 3.5 × 1 000 = 3 500 m.
   2. 2 400 ÷ 1 000 = 2.4 kg.
   3. 450 ÷ 100 = 4.5 m.
   4. 3.2 × 1 000 = 3 200 ml.
   5. 0.6 × 100 = 60 cm.

2. Answer to Question 2

   1. 12 × 2.5 = 30 cm.
   2. 15 miles = 3 × 5 miles, so 3 × 8 = 24 km.
   3. 5 × 2.2 = 11 pounds.
   4. 10 × 4.5 = 45 litres.
   5. 40 miles = 8 × 5 miles, so 8 × 8 = 64 km.

3. Answer to Question 3

   1. The perimeter is the distance all the way round: two lengths and two widths. \(P=2\times12+2\times7=24+14=\) 38 cm.
   2. A square has four equal sides: \(P=4\times8.5=34\). Think of it as \(4\times8=32\) plus \(4\times0.5=2\). Answer: 34 cm.
   3. Add one length and one width, then double: \(3.5+2.4=5.9\) and \(2\times5.9=\) 11.8 m.
   4. A regular hexagon has 6 equal sides: \(6\times6.5=36+3=\) 39 cm.

4. Answer to Question 4

   1. \(A=12\times7=\) 84 cm².
   2. Whole rectangle: \(10\times6=60\) cm². Corner: \(4\times3=12\) cm². Area left: \(60-12=\) 48 cm².
   3. \(A=9\times9=\) 81 cm².
   4. Width = area ÷ length = 54 ÷ 9 = 6 cm.

5. Answer to Question 5

   1. The area of a triangle is half of base × height: \(\frac{1}{2}\times8\times6=\frac{1}{2}\times48=\) 24 cm². It is half of the 8 cm by 6 cm rectangle around it.
   2. A parallelogram can be cut and rearranged into a rectangle, so area = base × perpendicular height: \(9\times5=\) 45 cm².
   3. \(11\times4=44\), and half of 44 is 22. Answer: 22 cm².
   4. Work backwards: \(\frac{1}{2}\times12=6\), so \(6h=30\) and \(h=30\div6=\) 5 cm. Check: \(\frac{1}{2}\times12\times5=30\).

6. Answer to Question 6

   1. \(V=5\times4\times3=\) 60 cm³.
   2. \(V=6\times6\times6=\) 216 cm³.
   3. Base area = 8 × 5 = 40 cm². Height = 120 ÷ 40 = 3 cm.
   4. \(V=50\times30\times40=60\,000\) cm³. 60 000 ÷ 1 000 = 60 litres.

7. Answer to Question 7

   1. 1.5 × 1 000 = 1 500 ml.
   2. 1 500 ÷ 250 = 6 glasses.
   3. 20 × 2 = 40 glasses. 40 × 250 = 10 000 ml = 10 litres.
   4. 10 ÷ 2 = 5 cartons.

8. Answer to Question 8

   1. 5 × 1 000 = 5 000 m.
   2. 5 000 ÷ 400 = 12.5 laps.
   3. He still has 1.5 km = 1 500 m to run. 1 500 ÷ 400 = 3.75, so 3.75 laps (almost 4 laps).
   4. 5 ÷ 1.6 = 3.125, so about 3.1 miles.

9. Answer to Question 9

   1. 130 km/h ÷ 8 × 5 = 16.25 × 5 = 81.25, so about 81 miles per hour.
   2. 290 km ÷ 1.6 = 181.25 miles. For each 40 miles the car uses 4.5 litres, so for 181.25 miles it uses 181.25 ÷ 40 × 4.5 = 20.4 litres (to 1 decimal place).
   3. 20.4 × £1.50 = £30.60.
   4. 120 ÷ 8 × 5 = 15 × 5 = 75 miles.

10. Answer to Question 10

    1. \(A=4.5\times3.2=\) 14.4 m².
    2. 14.4 × £12.50 = £180.
    3. \(P=2\times(4.5+3.2)=2\times7.7=\) 15.4 m.
    4. 15.4 − 0.9 = 14.5 m. 14.5 ÷ 2.4 = 6.04..., so he needs 7 lengths (6 lengths would be just short).

11. Answer to Question 11

    1. Whole lawn: 12 × 8 = 96 m². Pond: 3 × 3 = 9 m². Grass: 96 − 9 = 87 m².
    2. 87 ÷ 30 = 2.9, so he needs 3 kg.
    3. 3 × £6.50 = £19.50.
    4. Perimeter: 2 × (12 + 8) = 40 m. Cost: 40 × £8.40 = £336.

12. Answer to Question 12

    1. Half of the base is \(2.4\div2=1.2\), so \(A=1.2\times3.5=\) 4.2 m² (\(1\times3.5=3.5\) and \(0.2\times3.5=0.7\)).
    2. Two equal sails: \(2\times4.2=\) 8.4 m².
    3. \(8.4\times18=8\times18+0.4\times18=144+7.2=151.2\). The cloth costs £151.20.
    4. Half of the base is 1.5, so \(1.5h=6.3\) and \(h=6.3\div1.5=\) 4.2 m. Check: \(1.5\times4.2=6.3\).

13. Answer to Question 13

    1. Volume of a cuboid = length × width × height: \(60\times30=1\,800\) and \(1\,800\times35=63\,000\) cm³. As 1 000 cm³ = 1 litre, that is 63 litres.
    2. The water stops 5 cm below the 35 cm top: 35 − 5 = 30 cm.
    3. Use the water height: \(60\times30\times30=54\,000\) cm³ = 54 litres.
    4. Divide the water by the amount for one fish: 54 ÷ 4.5 = 12 (because 12 × 4.5 = 54). She can keep at most 12 fish.

14. Answer to Question 14

    1. 20 × 15 × 10 = 3 000 cm³.
    2. 60 × 45 × 30 = 81 000 cm³.
    3. 81 000 ÷ 3 000 = 27 boxes.
    4. Along the length: 60 ÷ 20 = 3. Along the width: 45 ÷ 15 = 3. Along the height: 30 ÷ 10 = 3. So 3 × 3 × 3 = 27 boxes, which agrees.

15. Answer to Question 15

    1. \(V=25\times10\times1.2=\) 300 m³.
    2. 300 × 1 000 = 300 000 litres.
    3. 300 000 ÷ 1 500 = 200 minutes = 3 hours 20 minutes.
    4. Area = 25 × 10 = 250 m². Cost = 250 × £14 = £3 500.
    5. The outer rectangle is (25 + 4) m by (10 + 4) m = 29 m by 14 m. Area = 29 × 14 = 406 m². The path area is 406 − 250 = 156 m².
    6. 156 × £22 = £3 432.

16. Answer to Question 16

    1. A: 4 × 4 = 16. B: 8 × 2 = 16. C: 16 × 1 = 16. All are 16 m².
    2. A: 2 × (4 + 4) = 16 m. B: 2 × (8 + 2) = 20 m. C: 2 × (16 + 1) = 34 m.
    3. Rectangle A (the square) needs the least fencing (16 m). Rectangle C needs the most (34 m).
    4. 34 − 16 = 18 m more. 18 × £9.50 = £171.
    5. Half the perimeter is 12 m, so length + width = 12: 1 by 11 (area 11), 2 by 10 (20), 3 by 9 (27), 4 by 8 (32), 5 by 7 (35) and 6 by 6 (36). The greatest area is 36 m², the 6 m by 6 m square.

17. Answer to Question 17

    1. Split the room into a bottom rectangle that is 10 m wide and 3.5 m high, and a top rectangle that is 6 m wide and 1.5 m high. Areas: 10 × 3.5 = 35 m² and 6 × 1.5 = 9 m². Total = 35 + 9 = 44 m². (Check: the 10 m by 5 m rectangle is 50 m², minus the missing corner 4 m by 1.5 m = 6 m², gives 44 m².)
    2. 44 × £18 = £792.
    3. The left side is 5 m and the bottom is 10 m. The top edges are 6 m and 4 m, which add to 10 m, and the right edges are 1.5 m and 3.5 m, which add to 5 m. Perimeter = 5 + 10 + 6 + 1.5 + 4 + 3.5 = 30 m.
    4. The rug has an area of 3 × 2 = 6 m². 6/44 = \(\frac{3}{22}\) of the floor.

18. Answer to Question 18

    1. \(A=40\times25=\) 1 000 m².
    2. \(A=\frac{1}{2}\times40\times18=\) 360 m².
    3. 1 000 + 360 = 1 360 m².
    4. 1 360 ÷ 10 000 = 0.136 hectares.
    5. 1 360 ÷ 100 = 13.6, so the farmer needs 14 bags. Cost: 14 × £12.50 = £175.

19. Answer to Question 19

    1. \(V=2\times1.5\times1=\) 3 m³.
    2. 3 × 1 000 = 3 000 litres.
    3. 3 000 ÷ 0.5 = 6 000 minutes. 6 000 ÷ 60 = 100 hours.
    4. \(\frac{3}{4}\) of 3 000 = 2 250 litres.
    5. 2 250 ÷ 12 = 187.5, so 187 full buckets.

20. Answer to Question 20

    1. Length + width = 30 ÷ 2 = 15, so the width is 15 − 9 = 6 cm. Area = 9 × 6 = 54 cm².
    2. Side = 30 ÷ 4 = 7.5 cm. Area = 7.5 × 7.5 = 56.25 cm².
    3. 56.25 − 54 = 2.25 cm².
    4. \(V=7.5\times7.5\times4=\) 225 cm³.