This figure is not drawn to scale. A rectangular glass container 72 cm by 56 cm by 49 cm has 2 compartments, T and U, with a water height of 38 cm in T and 11 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 38 x 56
= 42560 cm
3 Length of Compartment U
= 72 - 20
= 52 cm
Volume of the water in Compartment U
= 52 x 56 x 11
= 32032 cm
3 Total volume of water
= 42560 + 32032
= 74592 cm
3 Base area of the glass container
= 72 x 56
= 4032 cm
2 Height of water
= 74592 ÷ 4032
= 18.5 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment T
= 38 - 18.5
= 19.5 cm
Drop in the volume of Compartment T
= 56 x 20 x 19.5
= 21840 cm
3 Volume of water flowed from T to U in 1 minute
= 21840 ÷ 90
≈ 242.7 cm
3 Answer(s): (a) 18.5 cm; (b) 242.7 cm
3