This figure is not drawn to scale. A rectangular glass tank 81 cm by 50 cm by 40 cm has 2 compartments, B and C, with a water height of 39 cm in B and 12 cm in C. A hole in the slider caused water to leak from B to C. 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 B to C in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment B
= 39 x 39 x 50
= 76050 cm
3 Length of Compartment C
= 81 - 39
= 42 cm
Volume of the water in Compartment C
= 42 x 50 x 12
= 25200 cm
3 Total volume of water
= 76050 + 25200
= 101250 cm
3 Base area of the glass tank
= 81 x 50
= 4050 cm
2 Height of water
= 101250 ÷ 4050
= 25 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment B
= 39 - 25
= 14 cm
Drop in the volume of Compartment B
= 50 x 39 x 14
= 27300 cm
3 Volume of water flowed from B to C in 1 minute
= 27300 ÷ 90
≈ 303.3 cm
3 Answer(s): (a) 25 cm; (b) 303.3 cm
3