Millilitres, cubic centimetres and displacement worksheet

Part A: Working out and filling in

1. 1. 735

   How many mL does a space of 1 cm³ hold? Think whether the number changes.

   A space of 1 cm³ holds exactly 1 mL: the number stays the same, 735 mL.

2. 2. 2.1

   2100 cm³ is 2100 mL. 1000 mL make 1 L, so divide by 1000.

   2100 cm³ = 2100 mL; 1000 mL is 1 L, so 2100 ÷ 1000 = 2.1.

3. 3. 144 mL

   Find the inside volume first: length × width × height. 1 cm³ holds 1 mL.

   The inside is 8 × 6 × 3 = 144 cm³, and 1 cm³ holds 1 mL: 144 mL.

4. 4. 32 L

   Find the tank's inside volume first, 40 × 20 × 40 cm³, then change it into litres.

   40 × 20 × 40 = 32000 cm³ = 32000 mL; 32000 ÷ 1000 = 32 L.

5. 5. The water is 9 cm deep

   Depth = the water's volume ÷ the base's area, and 1 mL = 1 cm³: 25 × 8 = 200, 1800 ÷ 200 = 9, so 9 cm

6. 6. Water in the tank: 110 mL

   The water's volume = length × width × its depth (not the tank's height): 5 × 2 = 10, 10 × 11 = 110, and 110 cm³ = 110 mL, so 110 mL

7. 7. The water rises by 3 cm

   The water that rose has the stone's volume; divide by the base: 25 × 15 = 375, 1125 ÷ 375 = 3, so it rises 3 cm

8. 8. The water rises by 5 cm

   The water that rose has the stone's volume; divide by the base: 12 × 12 = 144, 720 ÷ 144 = 5, so it rises 5 cm

9. 9. Volume of the stone = 1500 cm³

   The water that rose takes up the stone's volume: 25 × 20 = 500, 500 × 3 = 1500, so 1500 cm³

10. 10. Water in the tank: 8 L

    The water's volume = length × width × its depth (not the tank's height): 50 × 10 = 500, 500 × 16 = 8000, so 8000 mL; 1 L = 1000 mL: 8000 ÷ 1000 = 8, so 8 L

Part B: Choose, or true or false

1. 11. B. 720 cm³

   How much space does 1 mL take up? Remember 1 mL = 1 cm³, and check the unit is a volume.

   1 mL = 1 cm³, so 720 mL of water takes up 720 cm³.

2. 12. False

   1 L = 1000 cm³. Change 4 L into cm³, add 400, and compare with 800.

   1 L = 1000 cm³ and 1 mL = 1 cm³: 4 × 1000 + 400 = 4400.

Part C: Word problems

Marking: 2 for the working, 1 for the answer, 1 for the sentence.

1. 13. 9 times

   5 cm³ is 5 mL. See how many lots of 5 mL there are in 45 mL.

   5 cm³ is 5 mL: 45 ÷ 5 = 9 times.

2. 14. 2 boxes

   First find how many mL one box holds, 10 × 10 × 10, and change 2 L into mL.

   Each box is 10 × 10 × 10 = 1000 cm³, 1000 mL; 2 L = 2000 mL, and 2000 ÷ 1000 = 2 boxes.

3. 15. 288 mL

   Find the inside volume first: 6 × 4 × 12 cm³. 1 cm³ holds 1 mL.

   6 × 4 × 12 = 288 cm³, which is 288 mL.

4. 16. A cuboid tank 20 cm long and 10 cm wide holds some water. When a stone is placed in the tank so that it is completely under the water, the water level rises by 3 cm. What is the stone's volume, in cubic centimetres? (Answer: 600 cm³)

   20 × 10 × 3 = 600

5. 17. A cuboid tank is 50 cm long and 15 cm wide, with water 5 cm deep in it. How many millilitres of water are in the tank? (Answer: 3750 mL)

   50 × 15 × 5 = 3750 cm³, and 1 cm³ = 1 mL

6. 18. A cuboid tank 40 cm long and 25 cm wide holds some water. When a stone is placed in the tank so that it is completely under the water, the water level rises by 4 cm. What is the stone's volume, in cubic centimetres? (Answer: 4000 cm³)

   40 × 25 × 4 = 4000