The figure is not drawn to scale. Container P and Container Q have base areas of 3500 cm
2 and 2500 cm
2 respectively. Water was poured into an empty rectangular Container P until it reached a height of 31 cm. Some of the water was then poured from Container P into Container Q 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 P.
- How many litres of water were poured into Container Q?
(a)
Volume of water in Container P
= 3500 x 31
= 108500 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 1.3 ℓ = 1300 cm
3 Total volume of Container P and Container Q
= 108500 + 1300
= 109800 cm
3 Total base area of Container P and Container Q
= 3500 + 2500
= 6000 cm²
Height of Container P after
= 109800 ÷ 6000
= 18.3 cm
(b)
Volume of water in Container Q after pouring
= 2500 x 18.3
= 45750 cm
3 Volume of water poured into Container Q
= 45750 - 2500
= 43250 cm
3 43250 mℓ = 43.25 ℓ
Answer(s): (a) 18.3 cm; (b) 43.25 ℓ