This figure is not drawn to scale. A rectangular glass tank 76 cm by 59 cm by 41 cm has 2 compartments, M and N, with a water height of 35 cm in M and 12 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
= 38 x 35 x 59
= 78470 cm
3 Length of Compartment N
= 76 - 38
= 38 cm
Volume of the water in Compartment N
= 38 x 59 x 12
= 26904 cm
3 Total volume of water
= 78470 + 26904
= 105374 cm
3 Base area of the glass tank
= 76 x 59
= 4484 cm
2 Height of water
= 105374 ÷ 4484
= 23.5 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment M
= 35 - 23.5
= 11.5 cm
Drop in the volume of Compartment M
= 59 x 38 x 11.5
= 25783 cm
3 Volume of water flowed from M to N in 1 minute
= 25783 ÷ 90
≈ 286.5 cm
3 Answer(s): (a) 23.5 cm; (b) 286.5 cm
3