This figure is not drawn to scale. A rectangular glass container 72 cm by 59 cm by 48 cm has 2 compartments, J and K, with a water height of 30 cm in J and 10 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 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 J to K in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment J
= 36 x 30 x 59
= 63720 cm
3 Length of Compartment K
= 72 - 36
= 36 cm
Volume of the water in Compartment K
= 36 x 59 x 10
= 21240 cm
3 Total volume of water
= 63720 + 21240
= 84960 cm
3 Base area of the glass container
= 72 x 59
= 4248 cm
2 Height of water
= 84960 ÷ 4248
= 20 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment J
= 30 - 20
= 10 cm
Drop in the volume of Compartment J
= 59 x 36 x 10
= 21240 cm
3 Volume of water flowed from J to K in 1 minute
= 21240 ÷ 75
≈ 283.2 cm
3 Answer(s): (a) 20 cm; (b) 283.2 cm
3