This figure is not drawn to scale. A rectangular glass container 75 cm by 57 cm by 50 cm has 2 compartments, Z and A, with a water height of 38 cm in Z and 13 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 115 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
= 30 x 38 x 57
= 64980 cm
3 Length of Compartment A
= 75 - 30
= 45 cm
Volume of the water in Compartment A
= 45 x 57 x 13
= 33345 cm
3 Total volume of water
= 64980 + 33345
= 98325 cm
3 Base area of the glass container
= 75 x 57
= 4275 cm
2 Height of water
= 98325 ÷ 4275
= 23 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment Z
= 38 - 23
= 15 cm
Drop in the volume of Compartment Z
= 57 x 30 x 15
= 25650 cm
3 Volume of water flowed from Z to A in 1 minute
= 25650 ÷ 72
≈ 356.3 cm
3 Answer(s): (a) 23 cm; (b) 356.3 cm
3