This figure is not drawn to scale. A rectangular glass container 90 cm by 55 cm by 49 cm has 2 compartments, Z and A, with a water height of 36 cm in Z and 18 cm in A. A hole in the slider caused water to leak from Z to A. 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 Z to A in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Z
= 12 x 36 x 55
= 23760 cm
3 Length of Compartment A
= 90 - 12
= 78 cm
Volume of the water in Compartment A
= 78 x 55 x 18
= 77220 cm
3 Total volume of water
= 23760 + 77220
= 100980 cm
3 Base area of the glass container
= 90 x 55
= 4950 cm
2 Height of water
= 100980 ÷ 4950
= 20.4 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment Z
= 36 - 20.4
= 15.6 cm
Drop in the volume of Compartment Z
= 55 x 12 x 15.6
= 10296 cm
3 Volume of water flowed from Z to A in 1 minute
= 10296 ÷ 75
≈ 137.3 cm
3 Answer(s): (a) 20.4 cm; (b) 137.3 cm
3