This figure is not drawn to scale. A rectangular glass container 88 cm by 56 cm by 47 cm has 2 compartments, J and K, with a water height of 35 cm in J and 11 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
= 22 x 35 x 56
= 43120 cm
3 Length of Compartment K
= 88 - 22
= 66 cm
Volume of the water in Compartment K
= 66 x 56 x 11
= 40656 cm
3 Total volume of water
= 43120 + 40656
= 83776 cm
3 Base area of the glass container
= 88 x 56
= 4928 cm
2 Height of water
= 83776 ÷ 4928
= 17 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment J
= 35 - 17
= 18 cm
Drop in the volume of Compartment J
= 56 x 22 x 18
= 22176 cm
3 Volume of water flowed from J to K in 1 minute
= 22176 ÷ 105
≈ 211.2 cm
3 Answer(s): (a) 17 cm; (b) 211.2 cm
3