This figure is not drawn to scale. A rectangular glass tank 88 cm by 59 cm by 45 cm has 2 compartments, C and D, with a water height of 31 cm in C and 20 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 31 x 59
= 43896 cm
3 Length of Compartment D
= 88 - 24
= 64 cm
Volume of the water in Compartment D
= 64 x 59 x 20
= 75520 cm
3 Total volume of water
= 43896 + 75520
= 119416 cm
3 Base area of the glass tank
= 88 x 59
= 5192 cm
2 Height of water
= 119416 ÷ 5192
= 23 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment C
= 31 - 23
= 8 cm
Drop in the volume of Compartment C
= 59 x 24 x 8
= 11328 cm
3 Volume of water flowed from C to D in 1 minute
= 11328 ÷ 72
≈ 157.3 cm
3 Answer(s): (a) 23 cm; (b) 157.3 cm
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