This figure is not drawn to scale. A rectangular glass tank 90 cm by 55 cm by 43 cm has 2 compartments, F and G, with a water height of 38 cm in F and 15 cm in G. A hole in the slider caused water to leak from F to G. 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 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 F to G in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment F
= 27 x 38 x 55
= 56430 cm
3 Length of Compartment G
= 90 - 27
= 63 cm
Volume of the water in Compartment G
= 63 x 55 x 15
= 51975 cm
3 Total volume of water
= 56430 + 51975
= 108405 cm
3 Base area of the glass tank
= 90 x 55
= 4950 cm
2 Height of water
= 108405 ÷ 4950
= 21.9 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment F
= 38 - 21.9
= 16.1 cm
Drop in the volume of Compartment F
= 55 x 27 x 16.1
= 23908.5 cm
3 Volume of water flowed from F to G in 1 minute
= 23908.5 ÷ 90
≈ 265.7 cm
3 Answer(s): (a) 21.9 cm; (b) 265.7 cm
3