A cubical tank of edge 50 cm contained some water to a height of 15 cm.
- Find the volume of water in the tank at first.
- A tap was then turned on for 16 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 15
= 37500 cm
3
(b)
Remaining height of the tank not filled with water before the tap was turned on
= 50 - 15
= 35 cm
Volume of water needed to fill the tank
= 50 x 50 x 35
= 87500 cm³
1 ℓ = 1000 mℓ
0.4 ℓ = 0.4 x 1000 = 400 mℓ
Volume of water filled by the tap in 16 min
= 16 x 400
= 6400 cm
3Volume of more water needed to fill the tank to the brim when the tap was turned off
= 87500 - 6400
= 81100 cm
3
81100 mℓ = 81100 ÷ 1000 = 81.1 ℓ
Volume of more water to fill the tank = 81.1 ℓ
Answer(s): (a) 37500 cm
3; (b) 81.1 ℓ