This figure is not drawn to scale. A rectangular glass tank 70 cm by 59 cm by 45 cm has 2 compartments, M and N, with a water height of 34 cm in M and 20 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 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 M to N in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment M
= 17 x 34 x 59
= 34102 cm
3 Length of Compartment N
= 70 - 17
= 53 cm
Volume of the water in Compartment N
= 53 x 59 x 20
= 62540 cm
3 Total volume of water
= 34102 + 62540
= 96642 cm
3 Base area of the glass tank
= 70 x 59
= 4130 cm
2 Height of water
= 96642 ÷ 4130
= 23.4 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment M
= 34 - 23.4
= 10.6 cm
Drop in the volume of Compartment M
= 59 x 17 x 10.6
= 10631.8 cm
3 Volume of water flowed from M to N in 1 minute
= 10631.8 ÷ 72
≈ 147.7 cm
3 Answer(s): (a) 23.4 cm; (b) 147.7 cm
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