This figure is not drawn to scale. A rectangular glass container 72 cm by 55 cm by 40 cm has 2 compartments, N and P, with a water height of 31 cm in N and 13 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
= 26 x 31 x 55
= 44330 cm
3 Length of Compartment P
= 72 - 26
= 46 cm
Volume of the water in Compartment P
= 46 x 55 x 13
= 32890 cm
3 Total volume of water
= 44330 + 32890
= 77220 cm
3 Base area of the glass container
= 72 x 55
= 3960 cm
2 Height of water
= 77220 ÷ 3960
= 19.5 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment N
= 31 - 19.5
= 11.5 cm
Drop in the volume of Compartment N
= 55 x 26 x 11.5
= 16445 cm
3 Volume of water flowed from N to P in 1 minute
= 16445 ÷ 75
≈ 219.3 cm
3 Answer(s): (a) 19.5 cm; (b) 219.3 cm
3