The figure is not drawn to scale. Container Y and Container Z have base areas of 1500 cm
2 and 1000 cm
2 respectively. Water was poured into an empty rectangular Container Y until it reached a height of 46 cm. Some of the water was then poured from Container Y into Container Z which contained 1.4 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
= 1500 x 46
= 69000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 1.4 ℓ = 1400 cm
3 Total volume of Container Y and Container Z
= 69000 + 1400
= 70400 cm
3 Total base area of Container Y and Container Z
= 1500 + 1000
= 2500 cm²
Height of Container Y after
= 70400 ÷ 2500
= 28.16 cm
(b)
Volume of water in Container Z after pouring
= 1000 x 28.16
= 28160 cm
3 Volume of water poured into Container Z
= 28160 - 1000
= 27160 cm
3 27160 mℓ = 27.16 ℓ
Answer(s): (a) 28.16 cm; (b) 27.16 ℓ