This figure is not drawn to scale. A rectangular glass tank 85 cm by 50 cm by 44 cm has 2 compartments, L and M, with a water height of 34 cm in L and 17 cm in M. A hole in the slider caused water to leak from L to M. 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 134 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 L to M in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment L
= 12 x 34 x 50
= 20400 cm
3 Length of Compartment M
= 85 - 12
= 73 cm
Volume of the water in Compartment M
= 73 x 50 x 17
= 62050 cm
3 Total volume of water
= 20400 + 62050
= 82450 cm
3 Base area of the glass tank
= 85 x 50
= 4250 cm
2 Height of water
= 82450 ÷ 4250
= 19.4 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment L
= 34 - 19.4
= 14.6 cm
Drop in the volume of Compartment L
= 50 x 12 x 14.6
= 8760 cm
3 Volume of water flowed from L to M in 1 minute
= 8760 ÷ 105
≈ 83.4 cm
3 Answer(s): (a) 19.4 cm; (b) 83.4 cm
3