This figure is not drawn to scale. A rectangular glass container 75 cm by 59 cm by 46 cm has 2 compartments, D and E, with a water height of 36 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 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 D to E in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment D
= 36 x 36 x 59
= 76464 cm
3 Length of Compartment E
= 75 - 36
= 39 cm
Volume of the water in Compartment E
= 39 x 59 x 14
= 32214 cm
3 Total volume of water
= 76464 + 32214
= 108678 cm
3 Base area of the glass container
= 75 x 59
= 4425 cm
2 Height of water
= 108678 ÷ 4425
= 24.56 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment D
= 36 - 24.56
= 11.44 cm
Drop in the volume of Compartment D
= 59 x 36 x 11.44
= 24298.56 cm
3 Volume of water flowed from D to E in 1 minute
= 24298.56 ÷ 75
≈ 324 cm
3 Answer(s): (a) 24.56 cm; (b) 324 cm
3