There was 21.6 litres of water altogether in container A and container B. The water level in container A was the same as container B. The base area of container A was 700 cm^2 and the base of container B has dimensions as shown.

  1. (a)

    What was the height of water in container B?

  2. (b)

    From which container should water be poured out from such that both containers would have the same amount of water? How much water should be poured?

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Worked solution

9(a)

1. Convert the total volume of water from litres to cubic centimetres

21.6 litres=21.6×1000=21600 cm321.6 \text{ litres} = 21.6 \times 1000 = 21600 \text{ cm}^3

2. Calculate the base area of container B

Base area of B=40×50=2000 cm2\text{Base area of B} = 40 \times 50 = 2000 \text{ cm}^2

3. Find the total base area of both containers

Total base area=700+2000=2700 cm2\text{Total base area} = 700 + 2000 = 2700 \text{ cm}^2

4. Calculate the common height of water in both containers

h=216002700=8 cmh = \frac{21600}{2700} = 8 \text{ cm}

Answer

88 cm

9(b)

1. Calculate the volume of water currently in container A.

From part (a), the common height h=8 cmh = 8\text{ cm}.
Volume in A =700×8=5600 cm3= 700 \times 8 = 5600\text{ cm}^3.

2. Calculate the volume of water currently in container B.

Volume in B =2000×8=16000 cm3= 2000 \times 8 = 16000\text{ cm}^3.

3. Determine the target volume for each container to have the same amount.

Total volume =21600 cm3= 21600\text{ cm}^3.
Target volume per container =21600÷2=10800 cm3= 21600 \div 2 = 10800\text{ cm}^3.

4. Identify which container to pour from and calculate the amount.

Since 16000>1080016000 > 10800, water must be poured out from container B.
Amount to pour =16000−10800=5200 cm3= 16000 - 10800 = 5200\text{ cm}^3.

Answer

Container B, 5200 cm35200\text{ cm}^3

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