This figure is not drawn to scale. A rectangular glass container 80 cm by 54 cm by 46 cm has 2 compartments, T and U, with a water height of 32 cm in T and 12 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 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 T to U in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment T
= 38 x 32 x 54
= 65664 cm
3 Length of Compartment U
= 80 - 38
= 42 cm
Volume of the water in Compartment U
= 42 x 54 x 12
= 27216 cm
3 Total volume of water
= 65664 + 27216
= 92880 cm
3 Base area of the glass container
= 80 x 54
= 4320 cm
2 Height of water
= 92880 ÷ 4320
= 21.5 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment T
= 32 - 21.5
= 10.5 cm
Drop in the volume of Compartment T
= 54 x 38 x 10.5
= 21546 cm
3 Volume of water flowed from T to U in 1 minute
= 21546 ÷ 72
≈ 299.3 cm
3 Answer(s): (a) 21.5 cm; (b) 299.3 cm
3