This figure is not drawn to scale. A rectangular glass tank 80 cm by 59 cm by 50 cm has 2 compartments, N and P, with a water height of 39 cm in N and 13 cm in P. A hole in the slider caused water to leak from N to P. It was found that the water level in both compartments became the same after some time.
- What is the height of water in the tank now?
- It took 112 h for the water in both compartments to reach the same level. Assuming that water leaked at a constant rate, how much water flowed from N to P in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment N
= 30 x 39 x 59
= 69030 cm
3 Length of Compartment P
= 80 - 30
= 50 cm
Volume of the water in Compartment P
= 50 x 59 x 13
= 38350 cm
3 Total volume of water
= 69030 + 38350
= 107380 cm
3 Base area of the glass tank
= 80 x 59
= 4720 cm
2 Height of water
= 107380 ÷ 4720
= 22.75 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment N
= 39 - 22.75
= 16.25 cm
Drop in the volume of Compartment N
= 59 x 30 x 16.25
= 28762.5 cm
3 Volume of water flowed from N to P in 1 minute
= 28762.5 ÷ 90
≈ 319.6 cm
3 Answer(s): (a) 22.75 cm; (b) 319.6 cm
3