The figure is not drawn to scale. Container Y and Container Z have base areas of 3000 cm
2 and 1000 cm
2 respectively. Water was poured into an empty rectangular Container Y until it reached a height of 49 cm. Some of the water was then poured from Container Y into Container Z which contained 2.6 ℓ of water until the height of the water in both containers were the same.
- Find the new height of the water in Container Y.
- How many litres of water were poured into Container Z?
(a)
Volume of water in Container Y
= 3000 x 49
= 147000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 2.6 ℓ = 2600 cm
3 Total volume of Container Y and Container Z
= 147000 + 2600
= 149600 cm
3 Total base area of Container Y and Container Z
= 3000 + 1000
= 4000 cm²
Height of Container Y after
= 149600 ÷ 4000
= 37.4 cm
(b)
Volume of water in Container Z after pouring
= 1000 x 37.4
= 37400 cm
3 Volume of water poured into Container Z
= 37400 - 1000
= 36400 cm
3 36400 mℓ = 36.4 ℓ
Answer(s): (a) 37.4 cm; (b) 36.4 ℓ