The figure is not drawn to scale. Container Q and Container R have base areas of 3000 cm
2 and 2000 cm
2 respectively. Water was poured into an empty rectangular Container Q until it reached a height of 44 cm. Some of the water was then poured from Container Q into Container R which contained 2.6 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
= 3000 x 44
= 132000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 2.6 ℓ = 2600 cm
3 Total volume of Container Q and Container R
= 132000 + 2600
= 134600 cm
3 Total base area of Container Q and Container R
= 3000 + 2000
= 5000 cm²
Height of Container Q after
= 134600 ÷ 5000
= 26.92 cm
(b)
Volume of water in Container R after pouring
= 2000 x 26.92
= 53840 cm
3 Volume of water poured into Container R
= 53840 - 2000
= 51840 cm
3 51840 mℓ = 51.84 ℓ
Answer(s): (a) 26.92 cm; (b) 51.84 ℓ