The figure is not drawn to scale. Tank D and Tank E have base areas of 4000 cm
2 and 3000 cm
2 respectively. Water was poured into an empty rectangular Tank D until it reached a height of 42 cm. Some of the water was then poured from Tank D into Tank E which contained 1.4 ℓ of water until the height of the water in both tanks were the same.
- Find the new height of the water in Tank D.
- How many litres of water were poured into Tank E?
(a)
Volume of water in Tank D
= 4000 x 42
= 168000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 1.4 ℓ = 1400 cm
3 Total volume of Tank D and Tank E
= 168000 + 1400
= 169400 cm
3 Total base area of Tank D and Tank E
= 4000 + 3000
= 7000 cm²
Height of Tank D after
= 169400 ÷ 7000
= 24.2 cm
(b)
Volume of water in Tank E after pouring
= 3000 x 24.2
= 72600 cm
3 Volume of water poured into Tank E
= 72600 - 3000
= 69600 cm
3 69600 mℓ = 69.6 ℓ
Answer(s): (a) 24.2 cm; (b) 69.6 ℓ