Two rectangular tanks, A and B, are used to hold water at a fish farm. Tank A has a base area of 20 cm² and its water level is 36 cm high. Tank B has a water level of 9 cm high. At first, the amount of water in Tank A is 5 times the amount of water in Tank B. Some water is then poured from Tank A into Tank B, and afterwards both tanks have water at the same height. Assume neither tank overflows.
- Find the base area of Tank B.
- Find the decrease in the water level of Tank A.
Need a hint?
For (a), first find the volume of water in Tank B using the 5 times ratio. For (b), the total water stays the same, so find the common height from the total volume and the two base areas.
Worked answer
- (a) Volume of water in A = 20 × 36 = 720 cm³.
- (a) Volume of water in B = 720 ÷ 5 = 144 cm³, so base area of B = 144 ÷ 9 = 16 cm².
- (b) Total water = 720 + 144 = 864 cm³, and combined base area = 20 + 16 = 36 cm².
- (b) Common water level = 864 ÷ 36 = 24 cm, so decrease in A = 36 − 24 = 12 cm.
The mistake this question tests
Stopped at one part in ratio
Pupils often use the height of Tank B (9 cm) as if it were the volume, or take the water level of Tank A after pouring (24 cm) as the answer to (b) instead of the decrease.
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