This figure is not drawn to scale. A rectangular glass tank 80 cm by 57 cm by 44 cm has 2 compartments, C and D, with a water height of 34 cm in C and 13 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 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 C to D in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment C
= 24 x 34 x 57
= 46512 cm
3 Length of Compartment D
= 80 - 24
= 56 cm
Volume of the water in Compartment D
= 56 x 57 x 13
= 41496 cm
3 Total volume of water
= 46512 + 41496
= 88008 cm
3 Base area of the glass tank
= 80 x 57
= 4560 cm
2 Height of water
= 88008 ÷ 4560
= 19.3 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment C
= 34 - 19.3
= 14.7 cm
Drop in the volume of Compartment C
= 57 x 24 x 14.7
= 20109.6 cm
3 Volume of water flowed from C to D in 1 minute
= 20109.6 ÷ 72
≈ 279.3 cm
3 Answer(s): (a) 19.3 cm; (b) 279.3 cm
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