This figure is not drawn to scale. A rectangular glass container 80 cm by 60 cm by 43 cm has 2 compartments, P and Q, with a water height of 30 cm in P and 14 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 container now?
- It took 115 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
= 22 x 30 x 60
= 39600 cm
3 Length of Compartment Q
= 80 - 22
= 58 cm
Volume of the water in Compartment Q
= 58 x 60 x 14
= 48720 cm
3 Total volume of water
= 39600 + 48720
= 88320 cm
3 Base area of the glass container
= 80 x 60
= 4800 cm
2 Height of water
= 88320 ÷ 4800
= 18.4 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment P
= 30 - 18.4
= 11.6 cm
Drop in the volume of Compartment P
= 60 x 22 x 11.6
= 15312 cm
3 Volume of water flowed from P to Q in 1 minute
= 15312 ÷ 72
≈ 212.7 cm
3 Answer(s): (a) 18.4 cm; (b) 212.7 cm
3