The figure is not drawn to scale. Container Z and Container A have base areas of 4000 cm
2 and 1000 cm
2 respectively. Water was poured into an empty rectangular Container Z until it reached a height of 50 cm. Some of the water was then poured from Container Z into Container A which contained 2.5 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
= 4000 x 50
= 200000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 2.5 ℓ = 2500 cm
3 Total volume of Container Z and Container A
= 200000 + 2500
= 202500 cm
3 Total base area of Container Z and Container A
= 4000 + 1000
= 5000 cm²
Height of Container Z after
= 202500 ÷ 5000
= 40.5 cm
(b)
Volume of water in Container A after pouring
= 1000 x 40.5
= 40500 cm
3 Volume of water poured into Container A
= 40500 - 1000
= 39500 cm
3 39500 mℓ = 39.5 ℓ
Answer(s): (a) 40.5 cm; (b) 39.5 ℓ