A cubical tank of edge 60 cm contained some water to a height of 20 cm.
- Find the volume of water in the tank at first.
- A tap was then turned on for 9 minutes to fill the tank with water at a rate of 0.4 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
= 60 x 60 x 20
= 72000 cm
3
(b)
Remaining height of the tank not filled with water before the tap was turned on
= 60 - 20
= 40 cm
Volume of water needed to fill the tank
= 60 x 60 x 40
= 144000 cm³
1 ℓ = 1000 mℓ
0.4 ℓ = 0.4 x 1000 = 400 mℓ
Volume of water filled by the tap in 9 min
= 9 x 400
= 3600 cm
3Volume of more water needed to fill the tank to the brim when the tap was turned off
= 144000 - 3600
= 140400 cm
3
140400 mℓ = 140400 ÷ 1000 = 140.4 ℓ
Volume of more water to fill the tank = 140.4 ℓ
Answer(s): (a) 72000 cm
3; (b) 140.4 ℓ