This figure is not drawn to scale. A rectangular glass tank 72 cm by 53 cm by 47 cm has 2 compartments, L and M, with a water height of 33 cm in L and 14 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 115 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
= 18 x 33 x 53
= 31482 cm
3 Length of Compartment M
= 72 - 18
= 54 cm
Volume of the water in Compartment M
= 54 x 53 x 14
= 40068 cm
3 Total volume of water
= 31482 + 40068
= 71550 cm
3 Base area of the glass tank
= 72 x 53
= 3816 cm
2 Height of water
= 71550 ÷ 3816
= 18.75 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment L
= 33 - 18.75
= 14.25 cm
Drop in the volume of Compartment L
= 53 x 18 x 14.25
= 13594.5 cm
3 Volume of water flowed from L to M in 1 minute
= 13594.5 ÷ 72
≈ 188.8 cm
3 Answer(s): (a) 18.75 cm; (b) 188.8 cm
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