The figure is not drawn to scale. Tank P and Tank Q have base areas of 4000 cm
2 and 2000 cm
2 respectively. Water was poured into an empty rectangular Tank P until it reached a height of 40 cm. Some of the water was then poured from Tank P into Tank Q which contained 2.6 ℓ of water until the height of the water in both tanks were the same.
- Find the new height of the water in Tank P.
- How many litres of water were poured into Tank Q?
(a)
Volume of water in Tank P
= 4000 x 40
= 160000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 2.6 ℓ = 2600 cm
3 Total volume of Tank P and Tank Q
= 160000 + 2600
= 162600 cm
3 Total base area of Tank P and Tank Q
= 4000 + 2000
= 6000 cm²
Height of Tank P after
= 162600 ÷ 6000
= 27.1 cm
(b)
Volume of water in Tank Q after pouring
= 2000 x 27.1
= 54200 cm
3 Volume of water poured into Tank Q
= 54200 - 2000
= 52200 cm
3 52200 mℓ = 52.2 ℓ
Answer(s): (a) 27.1 cm; (b) 52.2 ℓ