This figure is not drawn to scale. A rectangular glass tank 80 cm by 55 cm by 50 cm has 2 compartments, M and N, with a water height of 37 cm in M and 11 cm in N. A hole in the slider caused water to leak from M to N. 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 M to N in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment M
= 16 x 37 x 55
= 32560 cm
3 Length of Compartment N
= 80 - 16
= 64 cm
Volume of the water in Compartment N
= 64 x 55 x 11
= 38720 cm
3 Total volume of water
= 32560 + 38720
= 71280 cm
3 Base area of the glass tank
= 80 x 55
= 4400 cm
2 Height of water
= 71280 ÷ 4400
= 16.2 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment M
= 37 - 16.2
= 20.8 cm
Drop in the volume of Compartment M
= 55 x 16 x 20.8
= 18304 cm
3 Volume of water flowed from M to N in 1 minute
= 18304 ÷ 90
≈ 203.4 cm
3 Answer(s): (a) 16.2 cm; (b) 203.4 cm
3