Samira's rectangular aquarium has a base area of 2500 cm². It is initially 35 filled with water. Water flows into the aquarium from a hose at 7 litres per minute, and it takes 10 minutes to fill the aquarium to the brim.
- Find the full volume of the aquarium, in litres.
- Find the depth of the water before the hose was switched on.
Need a hint?
First find how much water the hose supplies in 10 minutes. This water fills only the empty part of the aquarium.
Worked answer
- Water added = 7 × 10 = 70 litres.
- The aquarium was 35 full, so the water added filled the empty 25.
- 25 of the aquarium = 70 litres, so 15 = 35 litres and the full volume = 5 × 35 = 175 litres.
- 175 litres = 175 000 cm³. Height of the aquarium = 175 000 ÷ 2500 = 70 cm.
- Depth before the hose was switched on = 35 × 70 = 42 cm.
Answer: 42 cm
The mistake this question tests
Habit
Fraction of a remainder
A common error is to treat the 70 litres added as the full capacity. Another error is to find only the depth occupied by the added water.
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