This figure is not drawn to scale. A rectangular glass tank 80 cm by 56 cm by 42 cm has 2 compartments, M and N, with a water height of 30 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 30 x 56
= 63840 cm
3 Length of Compartment N
= 80 - 38
= 42 cm
Volume of the water in Compartment N
= 42 x 56 x 12
= 28224 cm
3 Total volume of water
= 63840 + 28224
= 92064 cm
3 Base area of the glass tank
= 80 x 56
= 4480 cm
2 Height of water
= 92064 ÷ 4480
= 20.55 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment M
= 30 - 20.55
= 9.45 cm
Drop in the volume of Compartment M
= 56 x 38 x 9.45
= 20109.6 cm
3 Volume of water flowed from M to N in 1 minute
= 20109.6 ÷ 90
≈ 223.4 cm
3 Answer(s): (a) 20.55 cm; (b) 223.4 cm
3