The figure is not drawn to scale. Container Q and Container R have base areas of 2000 cm
2 and 1500 cm
2 respectively. Water was poured into an empty rectangular Container Q until it reached a height of 23 cm. Some of the water was then poured from Container Q into Container R which contained 1.6 ℓ of water until the height of the water in both containers were the same.
- Find the new height of the water in Container Q.
- How many litres of water were poured into Container R?
(a)
Volume of water in Container Q
= 2000 x 23
= 46000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 1.6 ℓ = 1600 cm
3 Total volume of Container Q and Container R
= 46000 + 1600
= 47600 cm
3 Total base area of Container Q and Container R
= 2000 + 1500
= 3500 cm²
Height of Container Q after
= 47600 ÷ 3500
= 13.6 cm
(b)
Volume of water in Container R after pouring
= 1500 x 13.6
= 20400 cm
3 Volume of water poured into Container R
= 20400 - 1500
= 18900 cm
3 18900 mℓ = 18.9 ℓ
Answer(s): (a) 13.6 cm; (b) 18.9 ℓ