This figure is not drawn to scale. A rectangular glass tank 90 cm by 58 cm by 46 cm has 2 compartments, T and U, with a water height of 36 cm in T and 14 cm in U. A hole in the slider caused water to leak from T to U. 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 T to U in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment T
= 18 x 36 x 58
= 37584 cm
3 Length of Compartment U
= 90 - 18
= 72 cm
Volume of the water in Compartment U
= 72 x 58 x 14
= 58464 cm
3 Total volume of water
= 37584 + 58464
= 96048 cm
3 Base area of the glass tank
= 90 x 58
= 5220 cm
2 Height of water
= 96048 ÷ 5220
= 18.4 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment T
= 36 - 18.4
= 17.6 cm
Drop in the volume of Compartment T
= 58 x 18 x 17.6
= 18374.4 cm
3 Volume of water flowed from T to U in 1 minute
= 18374.4 ÷ 105
≈ 175 cm
3 Answer(s): (a) 18.4 cm; (b) 175 cm
3