The figure is not drawn to scale. Tank Z and Tank A have base areas of 4000 cm
2 and 1000 cm
2 respectively. Water was poured into an empty rectangular Tank Z until it reached a height of 50 cm. Some of the water was then poured from Tank Z into Tank A 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 Z.
- How many litres of water were poured into Tank A?
(a)
Volume of water in Tank Z
= 4000 x 50
= 200000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 2.9 ℓ = 2900 cm
3 Total volume of Tank Z and Tank A
= 200000 + 2900
= 202900 cm
3 Total base area of Tank Z and Tank A
= 4000 + 1000
= 5000 cm²
Height of Tank Z after
= 202900 ÷ 5000
= 40.58 cm
(b)
Volume of water in Tank A after pouring
= 1000 x 40.58
= 40580 cm
3 Volume of water poured into Tank A
= 40580 - 1000
= 39580 cm
3 39580 mℓ = 39.58 ℓ
Answer(s): (a) 40.58 cm; (b) 39.58 ℓ