This figure is not drawn to scale. A rectangular glass tank 76 cm by 56 cm by 48 cm has 2 compartments, F and G, with a water height of 33 cm in F and 16 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
= 19 x 33 x 56
= 35112 cm
3 Length of Compartment G
= 76 - 19
= 57 cm
Volume of the water in Compartment G
= 57 x 56 x 16
= 51072 cm
3 Total volume of water
= 35112 + 51072
= 86184 cm
3 Base area of the glass tank
= 76 x 56
= 4256 cm
2 Height of water
= 86184 ÷ 4256
= 20.25 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment F
= 33 - 20.25
= 12.75 cm
Drop in the volume of Compartment F
= 56 x 19 x 12.75
= 13566 cm
3 Volume of water flowed from F to G in 1 minute
= 13566 ÷ 75
≈ 180.9 cm
3 Answer(s): (a) 20.25 cm; (b) 180.9 cm
3