This figure is not drawn to scale. A rectangular glass tank 80 cm by 55 cm by 40 cm has 2 compartments, M and N, with a water height of 37 cm in M and 16 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 114 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
= 40 x 37 x 55
= 81400 cm
3 Length of Compartment N
= 80 - 40
= 40 cm
Volume of the water in Compartment N
= 40 x 55 x 16
= 35200 cm
3 Total volume of water
= 81400 + 35200
= 116600 cm
3 Base area of the glass tank
= 80 x 55
= 4400 cm
2 Height of water
= 116600 ÷ 4400
= 26.5 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment M
= 37 - 26.5
= 10.5 cm
Drop in the volume of Compartment M
= 55 x 40 x 10.5
= 23100 cm
3 Volume of water flowed from M to N in 1 minute
= 23100 ÷ 75
≈ 308.0 cm
3 Answer(s): (a) 26.5 cm; (b) 308.0 cm
3