This figure is not drawn to scale. A rectangular glass container 70 cm by 51 cm by 50 cm has 2 compartments, C and D, with a water height of 40 cm in C and 19 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 114 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
= 17 x 40 x 51
= 34680 cm
3 Length of Compartment D
= 70 - 17
= 53 cm
Volume of the water in Compartment D
= 53 x 51 x 19
= 51357 cm
3 Total volume of water
= 34680 + 51357
= 86037 cm
3 Base area of the glass container
= 70 x 51
= 3570 cm
2 Height of water
= 86037 ÷ 3570
= 24.1 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment C
= 40 - 24.1
= 15.9 cm
Drop in the volume of Compartment C
= 51 x 17 x 15.9
= 13785.3 cm
3 Volume of water flowed from C to D in 1 minute
= 13785.3 ÷ 75
≈ 183.8 cm
3 Answer(s): (a) 24.1 cm; (b) 183.8 cm
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