This figure is not drawn to scale. A rectangular glass tank 90 cm by 59 cm by 42 cm has 2 compartments, N and P, with a water height of 32 cm in N and 18 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 134 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
= 36 x 32 x 59
= 67968 cm
3 Length of Compartment P
= 90 - 36
= 54 cm
Volume of the water in Compartment P
= 54 x 59 x 18
= 57348 cm
3 Total volume of water
= 67968 + 57348
= 125316 cm
3 Base area of the glass tank
= 90 x 59
= 5310 cm
2 Height of water
= 125316 ÷ 5310
= 23.6 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment N
= 32 - 23.6
= 8.4 cm
Drop in the volume of Compartment N
= 59 x 36 x 8.4
= 17841.6 cm
3 Volume of water flowed from N to P in 1 minute
= 17841.6 ÷ 105
≈ 169.9 cm
3 Answer(s): (a) 23.6 cm; (b) 169.9 cm
3