The figure is not drawn to scale. Container M and Container N have base areas of 3000 cm
2 and 1000 cm
2 respectively. Water was poured into an empty rectangular Container M until it reached a height of 42 cm. Some of the water was then poured from Container M into Container N which contained 2.4 ℓ of water until the height of the water in both containers were the same.
- Find the new height of the water in Container M.
- How many litres of water were poured into Container N?
(a)
Volume of water in Container M
= 3000 x 42
= 126000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 2.4 ℓ = 2400 cm
3 Total volume of Container M and Container N
= 126000 + 2400
= 128400 cm
3 Total base area of Container M and Container N
= 3000 + 1000
= 4000 cm²
Height of Container M after
= 128400 ÷ 4000
= 32.1 cm
(b)
Volume of water in Container N after pouring
= 1000 x 32.1
= 32100 cm
3 Volume of water poured into Container N
= 32100 - 1000
= 31100 cm
3 31100 mℓ = 31.1 ℓ
Answer(s): (a) 32.1 cm; (b) 31.1 ℓ