This figure is not drawn to scale. A rectangular glass container 84 cm by 60 cm by 44 cm has 2 compartments, T and U, with a water height of 36 cm in T and 15 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 134 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
= 33 x 36 x 60
= 71280 cm
3 Length of Compartment U
= 84 - 33
= 51 cm
Volume of the water in Compartment U
= 51 x 60 x 15
= 45900 cm
3 Total volume of water
= 71280 + 45900
= 117180 cm
3 Base area of the glass container
= 84 x 60
= 5040 cm
2 Height of water
= 117180 ÷ 5040
= 23.25 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment T
= 36 - 23.25
= 12.75 cm
Drop in the volume of Compartment T
= 60 x 33 x 12.75
= 25245 cm
3 Volume of water flowed from T to U in 1 minute
= 25245 ÷ 105
≈ 240.4 cm
3 Answer(s): (a) 23.25 cm; (b) 240.4 cm
3