The figure is not drawn to scale. Tank Y and Tank Z have base areas of 4000 cm
2 and 3000 cm
2 respectively. Water was poured into an empty rectangular Tank Y until it reached a height of 42 cm. Some of the water was then poured from Tank Y into Tank Z which contained 2.8 ℓ of water until the height of the water in both tanks were the same.
- Find the new height of the water in Tank Y.
- How many litres of water were poured into Tank Z?
(a)
Volume of water in Tank Y
= 4000 x 42
= 168000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 2.8 ℓ = 2800 cm
3 Total volume of Tank Y and Tank Z
= 168000 + 2800
= 170800 cm
3 Total base area of Tank Y and Tank Z
= 4000 + 3000
= 7000 cm²
Height of Tank Y after
= 170800 ÷ 7000
= 24.4 cm
(b)
Volume of water in Tank Z after pouring
= 3000 x 24.4
= 73200 cm
3 Volume of water poured into Tank Z
= 73200 - 3000
= 70200 cm
3 70200 mℓ = 70.2 ℓ
Answer(s): (a) 24.4 cm; (b) 70.2 ℓ