The figure is not drawn to scale. Tank X and Tank Y have base areas of 3000 cm
2 and 2000 cm
2 respectively. Water was poured into an empty rectangular Tank X until it reached a height of 50 cm. Some of the water was then poured from Tank X into Tank Y which contained 2.7 ℓ of water until the height of the water in both tanks were the same.
- Find the new height of the water in Tank X.
- How many litres of water were poured into Tank Y?
(a)
Volume of water in Tank X
= 3000 x 50
= 150000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 2.7 ℓ = 2700 cm
3 Total volume of Tank X and Tank Y
= 150000 + 2700
= 152700 cm
3 Total base area of Tank X and Tank Y
= 3000 + 2000
= 5000 cm²
Height of Tank X after
= 152700 ÷ 5000
= 30.54 cm
(b)
Volume of water in Tank Y after pouring
= 2000 x 30.54
= 61080 cm
3 Volume of water poured into Tank Y
= 61080 - 2000
= 59080 cm
3 59080 mℓ = 59.08 ℓ
Answer(s): (a) 30.54 cm; (b) 59.08 ℓ