A cubical tank of edge 40 cm contained some water to a height of 16 cm.
- Find the volume of water in the tank at first.
- A tap was then turned on for 13 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
= 40 x 40 x 16
= 25600 cm
3
(b)
Remaining height of the tank not filled with water before the tap was turned on
= 40 - 16
= 24 cm
Volume of water needed to fill the tank
= 40 x 40 x 24
= 38400 cm³
1 ℓ = 1000 mℓ
0.5 ℓ = 0.5 x 1000 = 500 mℓ
Volume of water filled by the tap in 13 min
= 13 x 500
= 6500 cm
3Volume of more water needed to fill the tank to the brim when the tap was turned off
= 38400 - 6500
= 31900 cm
3
31900 mℓ = 31900 ÷ 1000 = 31.9 ℓ
Volume of more water to fill the tank = 31.9 ℓ
Answer(s): (a) 25600 cm
3; (b) 31.9 ℓ
