A rectangular fish tank has length 100 cm, width 30 cm and height 40 cm.
It is filled with water to 90% of its capacity.
Find the volume of water in the fish tank, in litres.
1 litre = 1000 cm^3. Answer ___ A particular species of fish need 1600 cm^3 of water per fish.
What is the maximum number of such fish that could be kept in this fish tank? Answer ___ Given that this species of fish grow at a rate such that in each week the need for space increases by 200 cm^3 per fish.
How much space, in cm^3, does each fish need after one month? Answer ___ cm^3

1. Find the full capacity of the rectangular fish tank in cubic centimetres.

Volume of tank
$=100\times 30\times 40=120000\text{ cm}^3$

2. Find 90% of the capacity and convert to litres.

Volume of water
$=90\%\times 120000=0.9\times 120000=108000\text{ cm}^3$
Since $1000\text{ cm}^3=1$ litre,
$108000\div 1000=108\text{ litres}$

1. Use the volume of water from part (i) in cubic centimetres.

From part (i), the volume of water is $108$ litres.

Since $1$ litre $=1000\text{ cm}^3$,
$108\text{ litres}=108\times1000=108000\text{ cm}^3.$

2. Divide by the water needed per fish and take the greatest whole number.

Each fish needs $1600\text{ cm}^3$ of water.
$108000\div1600=67.5$

The maximum whole number of fish is therefore $67$.

1. Find the space needed after one month, taking one month as 4 weeks.

Initial space needed per fish $=1600\text{ cm}^3$

Increase in one month $=4\times 200=800\text{ cm}^3$

Space needed after one month $=1600+800=2400\text{ cm}^3$