GCSE · Units, money & time

Converting units (metric, time, area and volume)Exam-style questions

Change any measurement into the unit you need: know which way to go and by how much for length, mass, capacity and time, use a conversion you are given, square the factor for area and cube it for volume, turn cm³ into litres, read a scale, and choose a sensible unit in the first place.

Start practising Read the lesson

9 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 1Level 2Level 3Level 4
  1. 1
    (a) Change 3.53.5 m² into cm².

    (1 mark)
    (b) Change 82008200 cm² into m².

    (1 mark)
    Level 4 · 2 marksTry it
  2. 2
    Here is a question and an incorrect solution.

    Question:

    A rectangular rug measures 2.42.4 m by 1.51.5 m.

    Work out the area of the rug in cm².

    Solution:

    Area =2.4×1.5=3.6= 2.4 \times 1.5 = 3.6 m²

    11 m =100= 100 cm, so the area is 3.6×100=3603.6 \times 100 = 360 cm²

    Describe the error made and write out a correct solution.

    (3 marks)
    Level 4 · 3 marksTry it
  3. 3
    The diagram shows a piece of land in the shape of a right-angled triangle.300 m240 mNot to scale

    A charity plants trees on all of the land to make a new wood.

    It plants 16001600 trees per hectare.

    11 hectare =10 000= 10\,000 m²

    Work out the number of trees the charity plants.

    (4 marks)
    Level 4 · 4 marksTry it
  4. 4
    A water trough is in the shape of a cuboid.1.2 m40 cm45 cmNot drawn accurately

    The trough is filled with water using a bucket that holds 1212 litres.

    11 litre =1000= 1000 cm³
    (a) Assume that the trough is filled to the top.

    Work out how many buckets of water are needed.

    You must show your working.

    (4 marks)
    (b) In fact, the trough is only filled to a depth of 3535 cm.

    What does this mean about the number of buckets needed?

    Tick one box.
    • ☐ It is more than the answer to part (a)
    • ☐ It is the same as the answer to part (a)
    • ☐ It is less than the answer to part (a)
    • ☐ It is impossible to tell
    (1 mark)
    Level 4 · 5 marksTry it
  5. 5
    A raised flower bed is in the shape of a cuboid.2.4 m25 cm90 cmThe bed is to be filled with soil.

    Soil is sold in bags. Each bag holds 0.080.08 m³ of soil.

    Work out the least number of bags of soil needed to fill the bed.

    (3 marks)
    Level 4 · 3 marksTry it