This figure is not drawn to scale. A rectangular glass tank 80 cm by 55 cm by 40 cm has 2 compartments, S and T, with a water height of 31 cm in S and 15 cm in T. A hole in the slider caused water to leak from S to T. 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 S to T in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment S
= 29 x 31 x 55
= 49445 cm
3 Length of Compartment T
= 80 - 29
= 51 cm
Volume of the water in Compartment T
= 51 x 55 x 15
= 42075 cm
3 Total volume of water
= 49445 + 42075
= 91520 cm
3 Base area of the glass tank
= 80 x 55
= 4400 cm
2 Height of water
= 91520 ÷ 4400
= 20.8 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment S
= 31 - 20.8
= 10.2 cm
Drop in the volume of Compartment S
= 55 x 29 x 10.2
= 16269 cm
3 Volume of water flowed from S to T in 1 minute
= 16269 ÷ 90
≈ 180.8 cm
3 Answer(s): (a) 20.8 cm; (b) 180.8 cm
3