A cubical tank of edge 50 cm contained some water to a height of 13 cm.
- Find the volume of water in the tank at first.
- A tap was then turned on for 18 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
= 50 x 50 x 13
= 32500 cm
3
(b)
Remaining height of the tank not filled with water before the tap was turned on
= 50 - 13
= 37 cm
Volume of water needed to fill the tank
= 50 x 50 x 37
= 92500 cm³
1 ℓ = 1000 mℓ
0.5 ℓ = 0.5 x 1000 = 500 mℓ
Volume of water filled by the tap in 18 min
= 18 x 500
= 9000 cm
3Volume of more water needed to fill the tank to the brim when the tap was turned off
= 92500 - 9000
= 83500 cm
3
83500 mℓ = 83500 ÷ 1000 = 83.5 ℓ
Volume of more water to fill the tank = 83.5 ℓ
Answer(s): (a) 32500 cm
3; (b) 83.5 ℓ