This figure is not drawn to scale. A rectangular glass tank 90 cm by 55 cm by 41 cm has 2 compartments, T and U, with a water height of 31 cm in T and 13 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 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 T to U in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment T
= 33 x 31 x 55
= 56265 cm
3 Length of Compartment U
= 90 - 33
= 57 cm
Volume of the water in Compartment U
= 57 x 55 x 13
= 40755 cm
3 Total volume of water
= 56265 + 40755
= 97020 cm
3 Base area of the glass tank
= 90 x 55
= 4950 cm
2 Height of water
= 97020 ÷ 4950
= 19.6 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment T
= 31 - 19.6
= 11.4 cm
Drop in the volume of Compartment T
= 55 x 33 x 11.4
= 20691 cm
3 Volume of water flowed from T to U in 1 minute
= 20691 ÷ 90
≈ 229.9 cm
3 Answer(s): (a) 19.6 cm; (b) 229.9 cm
3