The figure is not drawn to scale. Container P and Container Q have base areas of 3000 cm
2 and 2000 cm
2 respectively. Water was poured into an empty rectangular Container P until it reached a height of 36 cm. Some of the water was then poured from Container P into Container Q which contained 2.8 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
= 3000 x 36
= 108000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 2.8 ℓ = 2800 cm
3 Total volume of Container P and Container Q
= 108000 + 2800
= 110800 cm
3 Total base area of Container P and Container Q
= 3000 + 2000
= 5000 cm²
Height of Container P after
= 110800 ÷ 5000
= 22.16 cm
(b)
Volume of water in Container Q after pouring
= 2000 x 22.16
= 44320 cm
3 Volume of water poured into Container Q
= 44320 - 2000
= 42320 cm
3 42320 mℓ = 42.32 ℓ
Answer(s): (a) 22.16 cm; (b) 42.32 ℓ