This figure is not drawn to scale. A rectangular glass container 76 cm by 58 cm by 43 cm has 2 compartments, T and U, with a water height of 39 cm in T and 18 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 114 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 39 x 58
= 85956 cm
3 Length of Compartment U
= 76 - 38
= 38 cm
Volume of the water in Compartment U
= 38 x 58 x 18
= 39672 cm
3 Total volume of water
= 85956 + 39672
= 125628 cm
3 Base area of the glass container
= 76 x 58
= 4408 cm
2 Height of water
= 125628 ÷ 4408
= 28.5 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment T
= 39 - 28.5
= 10.5 cm
Drop in the volume of Compartment T
= 58 x 38 x 10.5
= 23142 cm
3 Volume of water flowed from T to U in 1 minute
= 23142 ÷ 75
≈ 308.6 cm
3 Answer(s): (a) 28.5 cm; (b) 308.6 cm
3