This figure is not drawn to scale. A rectangular glass container 70 cm by 56 cm by 42 cm has 2 compartments, J and K, with a water height of 38 cm in J and 16 cm in K. A hole in the slider caused water to leak from J to K. 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 J to K in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment J
= 28 x 38 x 56
= 59584 cm
3 Length of Compartment K
= 70 - 28
= 42 cm
Volume of the water in Compartment K
= 42 x 56 x 16
= 37632 cm
3 Total volume of water
= 59584 + 37632
= 97216 cm
3 Base area of the glass container
= 70 x 56
= 3920 cm
2 Height of water
= 97216 ÷ 3920
= 24.8 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment J
= 38 - 24.8
= 13.2 cm
Drop in the volume of Compartment J
= 56 x 28 x 13.2
= 20697.6 cm
3 Volume of water flowed from J to K in 1 minute
= 20697.6 ÷ 105
≈ 197.1 cm
3 Answer(s): (a) 24.8 cm; (b) 197.1 cm
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