The figure is not drawn to scale. Tank M and Tank N have base areas of 2000 cm
2 and 1000 cm
2 respectively. Water was poured into an empty rectangular Tank M until it reached a height of 42 cm. Some of the water was then poured from Tank M into Tank N which contained 1.5 ℓ of water until the height of the water in both tanks were the same.
- Find the new height of the water in Tank M.
- How many litres of water were poured into Tank N?
(a)
Volume of water in Tank M
= 2000 x 42
= 84000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 1.5 ℓ = 1500 cm
3 Total volume of Tank M and Tank N
= 84000 + 1500
= 85500 cm
3 Total base area of Tank M and Tank N
= 2000 + 1000
= 3000 cm²
Height of Tank M after
= 85500 ÷ 3000
= 28.5 cm
(b)
Volume of water in Tank N after pouring
= 1000 x 28.5
= 28500 cm
3 Volume of water poured into Tank N
= 28500 - 1000
= 27500 cm
3 27500 mℓ = 27.5 ℓ
Answer(s): (a) 28.5 cm; (b) 27.5 ℓ