This figure is not drawn to scale. A rectangular glass tank 85 cm by 50 cm by 47 cm has 2 compartments, D and E, with a water height of 30 cm in D and 13 cm in E. A hole in the slider caused water to leak from D to E. 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 D to E in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment D
= 11 x 30 x 50
= 16500 cm
3 Length of Compartment E
= 85 - 11
= 74 cm
Volume of the water in Compartment E
= 74 x 50 x 13
= 48100 cm
3 Total volume of water
= 16500 + 48100
= 64600 cm
3 Base area of the glass tank
= 85 x 50
= 4250 cm
2 Height of water
= 64600 ÷ 4250
= 15.2 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment D
= 30 - 15.2
= 14.8 cm
Drop in the volume of Compartment D
= 50 x 11 x 14.8
= 8140 cm
3 Volume of water flowed from D to E in 1 minute
= 8140 ÷ 105
≈ 77.5 cm
3 Answer(s): (a) 15.2 cm; (b) 77.5 cm
3