This figure is not drawn to scale. A rectangular glass container 80 cm by 55 cm by 42 cm has 2 compartments, T and U, with a water height of 33 cm in T and 14 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 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 T to U in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment T
= 20 x 33 x 55
= 36300 cm
3 Length of Compartment U
= 80 - 20
= 60 cm
Volume of the water in Compartment U
= 60 x 55 x 14
= 46200 cm
3 Total volume of water
= 36300 + 46200
= 82500 cm
3 Base area of the glass container
= 80 x 55
= 4400 cm
2 Height of water
= 82500 ÷ 4400
= 18.75 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment T
= 33 - 18.75
= 14.25 cm
Drop in the volume of Compartment T
= 55 x 20 x 14.25
= 15675 cm
3 Volume of water flowed from T to U in 1 minute
= 15675 ÷ 90
≈ 174.2 cm
3 Answer(s): (a) 18.75 cm; (b) 174.2 cm
3