This figure is not drawn to scale. A rectangular glass container 77 cm by 56 cm by 41 cm has 2 compartments, Z and A, with a water height of 34 cm in Z and 12 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 34 x 56
= 53312 cm
3 Length of Compartment A
= 77 - 28
= 49 cm
Volume of the water in Compartment A
= 49 x 56 x 12
= 32928 cm
3 Total volume of water
= 53312 + 32928
= 86240 cm
3 Base area of the glass container
= 77 x 56
= 4312 cm
2 Height of water
= 86240 ÷ 4312
= 20 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment Z
= 34 - 20
= 14 cm
Drop in the volume of Compartment Z
= 56 x 28 x 14
= 21952 cm
3 Volume of water flowed from Z to A in 1 minute
= 21952 ÷ 90
≈ 243.9 cm
3 Answer(s): (a) 20 cm; (b) 243.9 cm
3