This figure is not drawn to scale. A rectangular glass tank 78 cm by 55 cm by 41 cm has 2 compartments, A and B, with a water height of 32 cm in A and 17 cm in B. A hole in the slider caused water to leak from A to B. 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 A to B in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment A
= 26 x 32 x 55
= 45760 cm
3 Length of Compartment B
= 78 - 26
= 52 cm
Volume of the water in Compartment B
= 52 x 55 x 17
= 48620 cm
3 Total volume of water
= 45760 + 48620
= 94380 cm
3 Base area of the glass tank
= 78 x 55
= 4290 cm
2 Height of water
= 94380 ÷ 4290
= 22 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment A
= 32 - 22
= 10 cm
Drop in the volume of Compartment A
= 55 x 26 x 10
= 14300 cm
3 Volume of water flowed from A to B in 1 minute
= 14300 ÷ 75
≈ 190.7 cm
3 Answer(s): (a) 22 cm; (b) 190.7 cm
3