The figure is not drawn to scale. Tank Q and Tank R have base areas of 3000 cm
2 and 1500 cm
2 respectively. Water was poured into an empty rectangular Tank Q until it reached a height of 46 cm. Some of the water was then poured from Tank Q into Tank R 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 Q.
- How many litres of water were poured into Tank R?
(a)
Volume of water in Tank Q
= 3000 x 46
= 138000 cm
3 (Base area x height)
1 ℓ = 1000 cm
3 1.5 ℓ = 1500 cm
3 Total volume of Tank Q and Tank R
= 138000 + 1500
= 139500 cm
3 Total base area of Tank Q and Tank R
= 3000 + 1500
= 4500 cm²
Height of Tank Q after
= 139500 ÷ 4500
= 31 cm
(b)
Volume of water in Tank R after pouring
= 1500 x 31
= 46500 cm
3 Volume of water poured into Tank R
= 46500 - 1500
= 45000 cm
3 45000 mℓ = 45 ℓ
Answer(s): (a) 31 cm; (b) 45 ℓ