The figure is not drawn to scale. Container X and Container Y have base areas of 2500 cm
2 and 1000 cm
2 respectively. Water was poured into an empty rectangular Container X until it reached a height of 47 cm. Some of the water was then poured from Container X into Container Y which contained 2.9 ℓ of water until the height of the water in both containers were the same.
- Find the new height of the water in Container X.
- How many litres of water were poured into Container Y?
(a)
Volume of water in Container X
= 2500 x 47
= 117500 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 2.9 ℓ = 2900 cm
3 Total volume of Container X and Container Y
= 117500 + 2900
= 120400 cm
3 Total base area of Container X and Container Y
= 2500 + 1000
= 3500 cm²
Height of Container X after
= 120400 ÷ 3500
= 34.4 cm
(b)
Volume of water in Container Y after pouring
= 1000 x 34.4
= 34400 cm
3 Volume of water poured into Container Y
= 34400 - 1000
= 33400 cm
3 33400 mℓ = 33.4 ℓ
Answer(s): (a) 34.4 cm; (b) 33.4 ℓ