The figure is not drawn to scale. Tank Y and Tank Z have base areas of 3000 cm
2 and 2000 cm
2 respectively. Water was poured into an empty rectangular Tank Y until it reached a height of 27 cm. Some of the water was then poured from Tank Y into Tank Z which contained 2.3 ℓ of water until the height of the water in both tanks were the same.
- Find the new height of the water in Tank Y.
- How many litres of water were poured into Tank Z?
(a)
Volume of water in Tank Y
= 3000 x 27
= 81000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 2.3 ℓ = 2300 cm
3 Total volume of Tank Y and Tank Z
= 81000 + 2300
= 83300 cm
3 Total base area of Tank Y and Tank Z
= 3000 + 2000
= 5000 cm²
Height of Tank Y after
= 83300 ÷ 5000
= 16.66 cm
(b)
Volume of water in Tank Z after pouring
= 2000 x 16.66
= 33320 cm
3 Volume of water poured into Tank Z
= 33320 - 2000
= 31320 cm
3 31320 mℓ = 31.32 ℓ
Answer(s): (a) 16.66 cm; (b) 31.32 ℓ