This figure is not drawn to scale. A rectangular glass container 84 cm by 53 cm by 47 cm has 2 compartments, T and U, with a water height of 37 cm in T and 16 cm in U. A hole in the slider caused water to leak from T to U. 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 134 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 T to U in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment T
= 38 x 37 x 53
= 74518 cm
3 Length of Compartment U
= 84 - 38
= 46 cm
Volume of the water in Compartment U
= 46 x 53 x 16
= 39008 cm
3 Total volume of water
= 74518 + 39008
= 113526 cm
3 Base area of the glass container
= 84 x 53
= 4452 cm
2 Height of water
= 113526 ÷ 4452
= 25.5 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment T
= 37 - 25.5
= 11.5 cm
Drop in the volume of Compartment T
= 53 x 38 x 11.5
= 23161 cm
3 Volume of water flowed from T to U in 1 minute
= 23161 ÷ 105
≈ 220.6 cm
3 Answer(s): (a) 25.5 cm; (b) 220.6 cm
3