The figure is not drawn to scale. Container Z and Container A have base areas of 3500 cm
2 and 1500 cm
2 respectively. Water was poured into an empty rectangular Container Z until it reached a height of 40 cm. Some of the water was then poured from Container Z into Container A 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 Z.
- How many litres of water were poured into Container A?
(a)
Volume of water in Container Z
= 3500 x 40
= 140000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 1.3 ℓ = 1300 cm
3 Total volume of Container Z and Container A
= 140000 + 1300
= 141300 cm
3 Total base area of Container Z and Container A
= 3500 + 1500
= 5000 cm²
Height of Container Z after
= 141300 ÷ 5000
= 28.26 cm
(b)
Volume of water in Container A after pouring
= 1500 x 28.26
= 42390 cm
3 Volume of water poured into Container A
= 42390 - 1500
= 40890 cm
3 40890 mℓ = 40.89 ℓ
Answer(s): (a) 28.26 cm; (b) 40.89 ℓ