This figure is not drawn to scale. A rectangular glass tank 75 cm by 55 cm by 48 cm has 2 compartments, P and Q, with a water height of 37 cm in P and 19 cm in Q. A hole in the slider caused water to leak from P to Q. 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 P to Q in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment P
= 28 x 37 x 55
= 56980 cm
3 Length of Compartment Q
= 75 - 28
= 47 cm
Volume of the water in Compartment Q
= 47 x 55 x 19
= 49115 cm
3 Total volume of water
= 56980 + 49115
= 106095 cm
3 Base area of the glass tank
= 75 x 55
= 4125 cm
2 Height of water
= 106095 ÷ 4125
= 25.72 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment P
= 37 - 25.72
= 11.28 cm
Drop in the volume of Compartment P
= 55 x 28 x 11.28
= 17371.2 cm
3 Volume of water flowed from P to Q in 1 minute
= 17371.2 ÷ 75
≈ 231.6 cm
3 Answer(s): (a) 25.72 cm; (b) 231.6 cm
3