This figure is not drawn to scale. A rectangular glass tank 78 cm by 53 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
= 15 x 37 x 53
= 29415 cm
3 Length of Compartment N
= 78 - 15
= 63 cm
Volume of the water in Compartment N
= 63 x 53 x 11
= 36729 cm
3 Total volume of water
= 29415 + 36729
= 66144 cm
3 Base area of the glass tank
= 78 x 53
= 4134 cm
2 Height of water
= 66144 ÷ 4134
= 16 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment M
= 37 - 16
= 21 cm
Drop in the volume of Compartment M
= 53 x 15 x 21
= 16695 cm
3 Volume of water flowed from M to N in 1 minute
= 16695 ÷ 90
≈ 185.5 cm
3 Answer(s): (a) 16 cm; (b) 185.5 cm
3