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 29 cm. Some of the water was then poured from Container Z into Container A which contained 1.2 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 29
= 116000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 1.2 ℓ = 1200 cm
3 Total volume of Container Z and Container A
= 116000 + 1200
= 117200 cm
3 Total base area of Container Z and Container A
= 4000 + 1000
= 5000 cm²
Height of Container Z after
= 117200 ÷ 5000
= 23.44 cm
(b)
Volume of water in Container A after pouring
= 1000 x 23.44
= 23440 cm
3 Volume of water poured into Container A
= 23440 - 1000
= 22440 cm
3 22440 mℓ = 22.44 ℓ
Answer(s): (a) 23.44 cm; (b) 22.44 ℓ