This figure is not drawn to scale. A rectangular glass container 70 cm by 55 cm by 40 cm has 2 compartments, C and D, with a water height of 40 cm in C and 14 cm in D. A hole in the slider caused water to leak from C to D. 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 112 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 C to D in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment C
= 14 x 40 x 55
= 30800 cm
3 Length of Compartment D
= 70 - 14
= 56 cm
Volume of the water in Compartment D
= 56 x 55 x 14
= 43120 cm
3 Total volume of water
= 30800 + 43120
= 73920 cm
3 Base area of the glass container
= 70 x 55
= 3850 cm
2 Height of water
= 73920 ÷ 3850
= 19.2 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment C
= 40 - 19.2
= 20.8 cm
Drop in the volume of Compartment C
= 55 x 14 x 20.8
= 16016 cm
3 Volume of water flowed from C to D in 1 minute
= 16016 ÷ 90
≈ 178 cm
3 Answer(s): (a) 19.2 cm; (b) 178 cm
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