The figure is not drawn to scale. Tank P and Tank Q have base areas of 4000 cm
2 and 1000 cm
2 respectively. Water was poured into an empty rectangular Tank P until it reached a height of 29 cm. Some of the water was then poured from Tank P into Tank Q which contained 2.9 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 29
= 116000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 2.9 ℓ = 2900 cm
3 Total volume of Tank P and Tank Q
= 116000 + 2900
= 118900 cm
3 Total base area of Tank P and Tank Q
= 4000 + 1000
= 5000 cm²
Height of Tank P after
= 118900 ÷ 5000
= 23.78 cm
(b)
Volume of water in Tank Q after pouring
= 1000 x 23.78
= 23780 cm
3 Volume of water poured into Tank Q
= 23780 - 1000
= 22780 cm
3 22780 mℓ = 22.78 ℓ
Answer(s): (a) 23.78 cm; (b) 22.78 ℓ