This figure is not drawn to scale. A rectangular glass container 76 cm by 56 cm by 49 cm has 2 compartments, U and V, with a water height of 39 cm in U and 20 cm in V. A hole in the slider caused water to leak from U to V. 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 U to V in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment U
= 14 x 39 x 56
= 30576 cm
3 Length of Compartment V
= 76 - 14
= 62 cm
Volume of the water in Compartment V
= 62 x 56 x 20
= 69440 cm
3 Total volume of water
= 30576 + 69440
= 100016 cm
3 Base area of the glass container
= 76 x 56
= 4256 cm
2 Height of water
= 100016 ÷ 4256
= 23.5 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment U
= 39 - 23.5
= 15.5 cm
Drop in the volume of Compartment U
= 56 x 14 x 15.5
= 12152 cm
3 Volume of water flowed from U to V in 1 minute
= 12152 ÷ 72
≈ 168.8 cm
3 Answer(s): (a) 23.5 cm; (b) 168.8 cm
3