The figure is not drawn to scale. Tank X and Tank Y have base areas of 4000 cm
2 and 1000 cm
2 respectively. Water was poured into an empty rectangular Tank X until it reached a height of 29 cm. Some of the water was then poured from Tank X into Tank Y which contained 2.7 ℓ of water until the height of the water in both tanks were the same.
- Find the new height of the water in Tank X.
- How many litres of water were poured into Tank Y?
(a)
Volume of water in Tank X
= 4000 x 29
= 116000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 2.7 ℓ = 2700 cm
3 Total volume of Tank X and Tank Y
= 116000 + 2700
= 118700 cm
3 Total base area of Tank X and Tank Y
= 4000 + 1000
= 5000 cm²
Height of Tank X after
= 118700 ÷ 5000
= 23.74 cm
(b)
Volume of water in Tank Y after pouring
= 1000 x 23.74
= 23740 cm
3 Volume of water poured into Tank Y
= 23740 - 1000
= 22740 cm
3 22740 mℓ = 22.74 ℓ
Answer(s): (a) 23.74 cm; (b) 22.74 ℓ