The figure is not drawn to scale. Container P and Container Q have base areas of 4000 cm
2 and 1000 cm
2 respectively. Water was poured into an empty rectangular Container P until it reached a height of 42 cm. Some of the water was then poured from Container P into Container Q which contained 2.9 ℓ of water until the height of the water in both containers were the same.
- Find the new height of the water in Container P.
- How many litres of water were poured into Container Q?
(a)
Volume of water in Container P
= 4000 x 42
= 168000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 2.9 ℓ = 2900 cm
3 Total volume of Container P and Container Q
= 168000 + 2900
= 170900 cm
3 Total base area of Container P and Container Q
= 4000 + 1000
= 5000 cm²
Height of Container P after
= 170900 ÷ 5000
= 34.18 cm
(b)
Volume of water in Container Q after pouring
= 1000 x 34.18
= 34180 cm
3 Volume of water poured into Container Q
= 34180 - 1000
= 33180 cm
3 33180 mℓ = 33.18 ℓ
Answer(s): (a) 34.18 cm; (b) 33.18 ℓ