This figure is not drawn to scale. A rectangular glass tank 80 cm by 53 cm by 49 cm has 2 compartments, F and G, with a water height of 34 cm in F and 17 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 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 F to G in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment F
= 40 x 34 x 53
= 72080 cm
3 Length of Compartment G
= 80 - 40
= 40 cm
Volume of the water in Compartment G
= 40 x 53 x 17
= 36040 cm
3 Total volume of water
= 72080 + 36040
= 108120 cm
3 Base area of the glass tank
= 80 x 53
= 4240 cm
2 Height of water
= 108120 ÷ 4240
= 25.5 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment F
= 34 - 25.5
= 8.5 cm
Drop in the volume of Compartment F
= 53 x 40 x 8.5
= 18020 cm
3 Volume of water flowed from F to G in 1 minute
= 18020 ÷ 75
≈ 240.3 cm
3 Answer(s): (a) 25.5 cm; (b) 240.3 cm
3