This figure is not drawn to scale. A rectangular glass container 80 cm by 55 cm by 45 cm has 2 compartments, M and N, with a water height of 35 cm in M and 17 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 container 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 M to N in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment M
= 10 x 35 x 55
= 19250 cm
3 Length of Compartment N
= 80 - 10
= 70 cm
Volume of the water in Compartment N
= 70 x 55 x 17
= 65450 cm
3 Total volume of water
= 19250 + 65450
= 84700 cm
3 Base area of the glass container
= 80 x 55
= 4400 cm
2 Height of water
= 84700 ÷ 4400
= 19.25 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment M
= 35 - 19.25
= 15.75 cm
Drop in the volume of Compartment M
= 55 x 10 x 15.75
= 8662.5 cm
3 Volume of water flowed from M to N in 1 minute
= 8662.5 ÷ 105
≈ 82.5 cm
3 Answer(s): (a) 19.25 cm; (b) 82.5 cm
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