This figure is not drawn to scale. A rectangular glass container 78 cm by 52 cm by 40 cm has 2 compartments, S and T, with a water height of 31 cm in S and 18 cm in T. A hole in the slider caused water to leak from S to T. 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 S to T in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment S
= 27 x 31 x 52
= 43524 cm
3 Length of Compartment T
= 78 - 27
= 51 cm
Volume of the water in Compartment T
= 51 x 52 x 18
= 47736 cm
3 Total volume of water
= 43524 + 47736
= 91260 cm
3 Base area of the glass container
= 78 x 52
= 4056 cm
2 Height of water
= 91260 ÷ 4056
= 22.5 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment S
= 31 - 22.5
= 8.5 cm
Drop in the volume of Compartment S
= 52 x 27 x 8.5
= 11934 cm
3 Volume of water flowed from S to T in 1 minute
= 11934 ÷ 72
≈ 165.8 cm
3 Answer(s): (a) 22.5 cm; (b) 165.8 cm
3