A cubical tank of edge 50 cm contained some water to a height of 14 cm.
- Find the volume of water in the tank at first.
- A tap was then turned on for 2 minutes to fill the tank with water at a rate of 0.8 ℓ per minute. How much more water was needed to fill the tank to the brim when the tap was turned off? Leave your answer in litres.
(a)
Volume of water in the tank at first
= 50 x 50 x 14
= 35000 cm
3
(b)
Remaining height of the tank not filled with water before the tap was turned on
= 50 - 14
= 36 cm
Volume of water needed to fill the tank
= 50 x 50 x 36
= 90000 cm³
1 ℓ = 1000 mℓ
0.8 ℓ = 0.8 x 1000 = 800 mℓ
Volume of water filled by the tap in 2 min
= 2 x 800
= 1600 cm
3Volume of more water needed to fill the tank to the brim when the tap was turned off
= 90000 - 1600
= 88400 cm
3
88400 mℓ = 88400 ÷ 1000 = 88.4 ℓ
Volume of more water to fill the tank = 88.4 ℓ
Answer(s): (a) 35000 cm
3; (b) 88.4 ℓ