A cubical tank of edge 50 cm contained some water to a height of 18 cm.
- Find the volume of water in the tank at first.
- A tap was then turned on for 15 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
= 50 x 50 x 18
= 45000 cm
3
(b)
Remaining height of the tank not filled with water before the tap was turned on
= 50 - 18
= 32 cm
Volume of water needed to fill the tank
= 50 x 50 x 32
= 80000 cm³
1 ℓ = 1000 mℓ
0.4 ℓ = 0.4 x 1000 = 400 mℓ
Volume of water filled by the tap in 15 min
= 15 x 400
= 6000 cm
3Volume of more water needed to fill the tank to the brim when the tap was turned off
= 80000 - 6000
= 74000 cm
3
74000 mℓ = 74000 ÷ 1000 = 74 ℓ
Volume of more water to fill the tank = 74 ℓ
Answer(s): (a) 45000 cm
3; (b) 74 ℓ
