A cubical tank of edge 20 cm contained some water to a height of 6 cm.
- Find the volume of water in the tank at first.
- A tap was then turned on for 12 minutes to fill the tank with water at a rate of 0.5 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
= 20 x 20 x 6
= 2400 cm
3
(b)
Remaining height of the tank not filled with water before the tap was turned on
= 20 - 6
= 14 cm
Volume of water needed to fill the tank
= 20 x 20 x 14
= 5600 cm³
1 ℓ = 1000 mℓ
0.5 ℓ = 0.5 x 1000 = 500 mℓ
Volume of water filled by the tap in 12 min
= 12 x 500
= 6000 cm
3Volume of more water needed to fill the tank to the brim when the tap was turned off
= 5600 - 6000
= -400 cm
3
-400 mℓ = -400 ÷ 1000 = -0.4 ℓ
Volume of more water to fill the tank = -0.4 ℓ
Answer(s): (a) 2400 cm
3; (b) -0.4 ℓ