This figure is not drawn to scale. A rectangular glass tank 75 cm by 56 cm by 43 cm has 2 compartments, N and P, with a water height of 32 cm in N and 17 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 tank now?
- It took 112 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
= 37 x 32 x 56
= 66304 cm
3 Length of Compartment P
= 75 - 37
= 38 cm
Volume of the water in Compartment P
= 38 x 56 x 17
= 36176 cm
3 Total volume of water
= 66304 + 36176
= 102480 cm
3 Base area of the glass tank
= 75 x 56
= 4200 cm
2 Height of water
= 102480 ÷ 4200
= 24.4 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment N
= 32 - 24.4
= 7.6 cm
Drop in the volume of Compartment N
= 56 x 37 x 7.6
= 15747.2 cm
3 Volume of water flowed from N to P in 1 minute
= 15747.2 ÷ 90
≈ 175 cm
3 Answer(s): (a) 24.4 cm; (b) 175 cm
3