This figure is not drawn to scale. A rectangular glass tank 84 cm by 57 cm by 48 cm has 2 compartments, M and N, with a water height of 39 cm in M and 18 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
= 15 x 39 x 57
= 33345 cm
3 Length of Compartment N
= 84 - 15
= 69 cm
Volume of the water in Compartment N
= 69 x 57 x 18
= 70794 cm
3 Total volume of water
= 33345 + 70794
= 104139 cm
3 Base area of the glass tank
= 84 x 57
= 4788 cm
2 Height of water
= 104139 ÷ 4788
= 21.75 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment M
= 39 - 21.75
= 17.25 cm
Drop in the volume of Compartment M
= 57 x 15 x 17.25
= 14748.75 cm
3 Volume of water flowed from M to N in 1 minute
= 14748.75 ÷ 90
≈ 163.9 cm
3 Answer(s): (a) 21.75 cm; (b) 163.9 cm
3