Capacity and volume worksheet

Part A: Working out and filling in

1. 1. The water is 4 cm deep

   Depth = the water's volume ÷ the base's area, and 1 mL = 1 cm³: 25 × 10 = 250, 1000 ÷ 250 = 4, so 4 cm

2. 2. The water is 11 cm deep

   Depth = the water's volume ÷ the base's area, and 1 mL = 1 cm³: 20 × 20 = 400, 4400 ÷ 400 = 11, so 11 cm

3. 3. Water in the tank: 21 L

   The water's volume = length × width × its depth (not the tank's height): 50 × 30 = 1500, 1500 × 14 = 21000, so 21000 mL; 1 L = 1000 mL: 21000 ÷ 1000 = 21, so 21 L

4. 4. Capacity of the tank = 546 mL

   Capacity = inside length × width × height: 13 × 7 = 91, 91 × 6 = 546, and 546 cm³ = 546 mL, so 546 mL

5. 5. The water is 12 cm deep

   Depth = the water's volume ÷ the base's area, and 1 mL = 1 cm³: In mL first, 15 × 1000 = 15000; 50 × 25 = 1250, 15000 ÷ 1250 = 12, so 12 cm

6. 6. Capacity of the tank = 1 L

   Capacity = inside length × width × height: 10 × 10 = 100, 100 × 10 = 1000, so 1000 mL; 1 L = 1000 mL: 1000 ÷ 1000 = 1, so 1 L

7. 7. Volume of the stone = 900 cm³

   The water that rose takes up the stone's volume: 15 × 15 = 225, 225 × 4 = 900, so 900 cm³

8. 8. Volume of the stone = 900 cm³

   The water that rose takes up the stone's volume: 30 × 10 = 300, 300 × 3 = 900, so 900 cm³

9. 9. Water in the tank: 18 L

   The water's volume = length × width × its depth (not the tank's height): 30 × 30 = 900, 900 × 20 = 18000, so 18000 mL; 1 L = 1000 mL: 18000 ÷ 1000 = 18, so 18 L

10. 10. Volume of the stone = 400 cm³

    The water that rose takes up the stone's volume: 25 × 8 = 200, 200 × 2 = 400, so 400 cm³

11. 11. Volume of the stone = 1800 cm³

    The water that rose takes up the stone's volume: 30 × 12 = 360, 360 × 5 = 1800, so 1800 cm³

12. 12. Volume of the stone = 1125 cm³

    The water that rose takes up the stone's volume: 25 × 15 = 375, 375 × 3 = 1125, so 1125 cm³

Part B: Word problems

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

1. 13. A cuboid tank 45 cm long and 20 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: 2700 cm³)

   45 × 20 × 3 = 2700

2. 14. A cuboid tank is 45 cm long and 40 cm wide, with water 29 cm deep in it. How many millilitres of water are in the tank? (Answer: 52200 mL)

   45 × 40 × 29 = 52200 cm³, and 1 cm³ = 1 mL

3. 15. A cuboid tank is 50 cm long and 35 cm wide, with water 19 cm deep in it. How many millilitres of water are in the tank? (Answer: 33250 mL)

   50 × 35 × 19 = 33250 cm³, and 1 cm³ = 1 mL

4. 16. A cuboid tank measures 80 cm long, 30 cm wide and 20 cm high inside. How many litres of water can it hold? (Answer: 48 L)

   80 × 30 × 20 = 48000; 80 × 30 × 20 ÷ 1000 = 48

5. 17. A cuboid tank 50 cm long and 30 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 1 cm. What is the stone's volume, in cubic centimetres? (Answer: 1500 cm³)

   50 × 30 × 1 = 1500

6. 18. An open wooden box with no lid is a cuboid 40 cm long, 18 cm wide and 25 cm high on the outside, made of boards 3 cm thick. What is the box's capacity, in cubic centimetres? (Answer: 8976 cm³)

   Inside: length 40 − 2 × 3 = 34, width 18 − 2 × 3 = 12, height 25 − 3 = 22 (no lid, so only the bottom board comes off); 34 × 12 × 22 = 8976 cm³