This figure is not drawn to scale. A rectangular glass container 80 cm by 51 cm by 46 cm has 2 compartments, Z and A, with a water height of 40 cm in Z and 10 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 112 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
= 28 x 40 x 51
= 57120 cm
3 Length of Compartment A
= 80 - 28
= 52 cm
Volume of the water in Compartment A
= 52 x 51 x 10
= 26520 cm
3 Total volume of water
= 57120 + 26520
= 83640 cm
3 Base area of the glass container
= 80 x 51
= 4080 cm
2 Height of water
= 83640 ÷ 4080
= 20.5 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment Z
= 40 - 20.5
= 19.5 cm
Drop in the volume of Compartment Z
= 51 x 28 x 19.5
= 27846 cm
3 Volume of water flowed from Z to A in 1 minute
= 27846 ÷ 90
≈ 309.4 cm
3 Answer(s): (a) 20.5 cm; (b) 309.4 cm
3