This figure is not drawn to scale. A rectangular glass container 80 cm by 51 cm by 50 cm has 2 compartments, N and P, with a water height of 34 cm in N and 10 cm in P. A hole in the slider caused water to leak from N to P. 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 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 N to P in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment N
= 35 x 34 x 51
= 60690 cm
3 Length of Compartment P
= 80 - 35
= 45 cm
Volume of the water in Compartment P
= 45 x 51 x 10
= 22950 cm
3 Total volume of water
= 60690 + 22950
= 83640 cm
3 Base area of the glass container
= 80 x 51
= 4080 cm
2 Height of water
= 83640 ÷ 4080
= 20.5 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment N
= 34 - 20.5
= 13.5 cm
Drop in the volume of Compartment N
= 51 x 35 x 13.5
= 24097.5 cm
3 Volume of water flowed from N to P in 1 minute
= 24097.5 ÷ 75
≈ 321.3 cm
3 Answer(s): (a) 20.5 cm; (b) 321.3 cm
3