This figure is not drawn to scale. A rectangular glass container 74 cm by 51 cm by 49 cm has 2 compartments, E and F, with a water height of 34 cm in E and 18 cm in F. A hole in the slider caused water to leak from E to F. 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 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 E to F in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment E
= 37 x 34 x 51
= 64158 cm
3 Length of Compartment F
= 74 - 37
= 37 cm
Volume of the water in Compartment F
= 37 x 51 x 18
= 33966 cm
3 Total volume of water
= 64158 + 33966
= 98124 cm
3 Base area of the glass container
= 74 x 51
= 3774 cm
2 Height of water
= 98124 ÷ 3774
= 26 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment E
= 34 - 26
= 8 cm
Drop in the volume of Compartment E
= 51 x 37 x 8
= 15096 cm
3 Volume of water flowed from E to F in 1 minute
= 15096 ÷ 105
≈ 143.8 cm
3 Answer(s): (a) 26 cm; (b) 143.8 cm
3