This figure is not drawn to scale. A rectangular glass tank 78 cm by 54 cm by 44 cm has 2 compartments, D and E, with a water height of 32 cm in D and 14 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
= 13 x 32 x 54
= 22464 cm
3 Length of Compartment E
= 78 - 13
= 65 cm
Volume of the water in Compartment E
= 65 x 54 x 14
= 49140 cm
3 Total volume of water
= 22464 + 49140
= 71604 cm
3 Base area of the glass tank
= 78 x 54
= 4212 cm
2 Height of water
= 71604 ÷ 4212
= 17 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment D
= 32 - 17
= 15 cm
Drop in the volume of Compartment D
= 54 x 13 x 15
= 10530 cm
3 Volume of water flowed from D to E in 1 minute
= 10530 ÷ 105
≈ 100.3 cm
3 Answer(s): (a) 17 cm; (b) 100.3 cm
3