This figure is not drawn to scale. A rectangular glass tank 70 cm by 52 cm by 43 cm has 2 compartments, E and F, with a water height of 39 cm in E and 11 cm in F. A hole in the slider caused water to leak from E to F. 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 134 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 E to F in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment E
= 11 x 39 x 52
= 22308 cm
3 Length of Compartment F
= 70 - 11
= 59 cm
Volume of the water in Compartment F
= 59 x 52 x 11
= 33748 cm
3 Total volume of water
= 22308 + 33748
= 56056 cm
3 Base area of the glass tank
= 70 x 52
= 3640 cm
2 Height of water
= 56056 ÷ 3640
= 15.4 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment E
= 39 - 15.4
= 23.6 cm
Drop in the volume of Compartment E
= 52 x 11 x 23.6
= 13499.2 cm
3 Volume of water flowed from E to F in 1 minute
= 13499.2 ÷ 105
≈ 128.6 cm
3 Answer(s): (a) 15.4 cm; (b) 128.6 cm
3