This figure is not drawn to scale. A rectangular glass container 75 cm by 55 cm by 50 cm has 2 compartments, M and N, with a water height of 39 cm in M and 14 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 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
= 24 x 39 x 55
= 51480 cm
3 Length of Compartment N
= 75 - 24
= 51 cm
Volume of the water in Compartment N
= 51 x 55 x 14
= 39270 cm
3 Total volume of water
= 51480 + 39270
= 90750 cm
3 Base area of the glass container
= 75 x 55
= 4125 cm
2 Height of water
= 90750 ÷ 4125
= 22 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment M
= 39 - 22
= 17 cm
Drop in the volume of Compartment M
= 55 x 24 x 17
= 22440 cm
3 Volume of water flowed from M to N in 1 minute
= 22440 ÷ 72
≈ 311.7 cm
3 Answer(s): (a) 22 cm; (b) 311.7 cm
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