The volume of an Olympic size swimming pool is 660 000 gallons. 1 gallon is approximately 3790 cm^3.

  1. (a)

    Convert 660 000 gallons to cm^3, leaving your answer in standard form.

    Answer ... cm^3

  2. (b)

    The average volume of water flowing from tap A and tap B are 8×1028\times10^{2} litres per minute and 1.2×1031.2\times10^{3} litres per minute respectively. Both taps are used to fill up the Olympic size swimming pool together. Calculate the time needed to fill up the pool completely.

    Answer ... minutes

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Worked solution

3(a)

1. Convert gallons to cubic centimetres and express in standard form

660 000×3790=2 501 400 000660\,000\times3790=2\,501\,400\,000
2 501 400 000=2.5014×1092\,501\,400\,000=2.5014\times10^{9}

Answer

2.5014×109 cm32.5014\times10^{9}\text{ cm}^3

3(b)

1. Convert the pool volume from cubic centimetres to litres

From part (a), the volume of the pool is
2.5014×109 cm3.2.5014\times10^{9}\text{ cm}^3.
Since 1000 cm3=11000\text{ cm}^3=1 litre,
2.5014×109÷1000=2.5014×106 litres.2.5014\times10^{9}\div1000=2.5014\times10^{6}\text{ litres}.

2. Find the combined flow rate and calculate the time taken

Combined flow rate
=8×102+1.2×103=8\times10^{2}+1.2\times10^{3}
=800+1200=2000 litres per minute.=800+1200=2000\text{ litres per minute}.
Time needed
=2.5014×1062000=1250.7 minutes.=\frac{2.5014\times10^{6}}{2000}=1250.7\text{ minutes}.

Answer

1250.71250.7 minutes

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