The figure is not drawn to scale. Container Z and Container A have base areas of 4000 cm
2 and 3500 cm
2 respectively. Water was poured into an empty rectangular Container Z until it reached a height of 32 cm. Some of the water was then poured from Container Z into Container A 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 Z.
- How many litres of water were poured into Container A?
(a)
Volume of water in Container Z
= 4000 x 32
= 128000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 2.8 ℓ = 2800 cm
3 Total volume of Container Z and Container A
= 128000 + 2800
= 130800 cm
3 Total base area of Container Z and Container A
= 4000 + 3500
= 7500 cm²
Height of Container Z after
= 130800 ÷ 7500
= 17.44 cm
(b)
Volume of water in Container A after pouring
= 3500 x 17.44
= 61040 cm
3 Volume of water poured into Container A
= 61040 - 3500
= 57540 cm
3 57540 mℓ = 57.54 ℓ
Answer(s): (a) 17.44 cm; (b) 57.54 ℓ