This figure is not drawn to scale. A rectangular glass tank 78 cm by 58 cm by 45 cm has 2 compartments, B and C, with a water height of 31 cm in B and 17 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 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 B to C in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment B
= 39 x 31 x 58
= 70122 cm
3 Length of Compartment C
= 78 - 39
= 39 cm
Volume of the water in Compartment C
= 39 x 58 x 17
= 38454 cm
3 Total volume of water
= 70122 + 38454
= 108576 cm
3 Base area of the glass tank
= 78 x 58
= 4524 cm
2 Height of water
= 108576 ÷ 4524
= 24 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment B
= 31 - 24
= 7 cm
Drop in the volume of Compartment B
= 58 x 39 x 7
= 15834 cm
3 Volume of water flowed from B to C in 1 minute
= 15834 ÷ 75
≈ 211.1 cm
3 Answer(s): (a) 24 cm; (b) 211.1 cm
3