Two rectangular fish tanks, X and Y, contain water. The base of tank X measures 25 cm by 8 cm. The base of tank Y measures 20 cm by 15 cm. Tank Y contained 2900 cm³ more water than tank X. The height of the water level in tank Y was 5 cm more than that in tank X.
- Find the height of the water level in tank X.
- Mia then poured some water from tank Y into tank X until the water level in both tanks was at the same height. How much water did she pour from tank Y into tank X?
Need a hint?
In (a), cut the water in Y into a bottom layer as high as the water in X and a 5 cm top layer. In (b), the total amount of water stays the same, so find the new height using both bases together.
Worked answer
- (a) Base area of X = 25 × 8 = 200 cm². Base area of Y = 20 × 15 = 300 cm².
- Let the height of water in X be h cm. Then the height in Y is (h + 5) cm.
- Split the water in Y into two layers. The bottom layer is h cm high and the top layer is 5 cm high.
- Volume of the top layer = 300 × 5 = 1500 cm³.
- Y's bottom layer has 300h cm³ and X has 200h cm³, so this layer gives Y 300h − 200h = 100h cm³ more.
- The rest of the difference is 2900 − 1500 = 1400 cm³, so 100h = 1400 and h = 14. The height of the water level in X is 14 cm.
- (b) Water in X at first = 200 × 14 = 2800 cm³. Height in Y = 14 + 5 = 19 cm, so water in Y = 300 × 19 = 5700 cm³.
- Total water = 2800 + 5700 = 8500 cm³. When the levels are equal, the water fills a combined base of 200 + 300 = 500 cm².
- Final height = 8500 ÷ 500 = 17 cm.
- Water poured into X = 200 × 17 − 2800 = 3400 − 2800 = 600 cm³.
The mistake this question tests
Left out the units
Many pupils divide 2900 by the difference in base areas (300 - 200) and get 29 cm. This ignores that Y's water is also 5 cm higher, which adds an extra 1500 cm³ to Y.
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See the answer →Practise PSLE area & volume until the mistakes stop.
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