The figure is not drawn to scale. Container X and Container Y have base areas of 3500 cm
2 and 2500 cm
2 respectively. Water was poured into an empty rectangular Container X until it reached a height of 49 cm. Some of the water was then poured from Container X into Container Y which contained 1.3 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
= 3500 x 49
= 171500 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 1.3 ℓ = 1300 cm
3 Total volume of Container X and Container Y
= 171500 + 1300
= 172800 cm
3 Total base area of Container X and Container Y
= 3500 + 2500
= 6000 cm²
Height of Container X after
= 172800 ÷ 6000
= 28.8 cm
(b)
Volume of water in Container Y after pouring
= 2500 x 28.8
= 72000 cm
3 Volume of water poured into Container Y
= 72000 - 2500
= 69500 cm
3 69500 mℓ = 69.5 ℓ
Answer(s): (a) 28.8 cm; (b) 69.5 ℓ