This figure is not drawn to scale. A rectangular glass container 88 cm by 51 cm by 48 cm has 2 compartments, S and T, with a water height of 32 cm in S and 10 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 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 S to T in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment S
= 40 x 32 x 51
= 65280 cm
3 Length of Compartment T
= 88 - 40
= 48 cm
Volume of the water in Compartment T
= 48 x 51 x 10
= 24480 cm
3 Total volume of water
= 65280 + 24480
= 89760 cm
3 Base area of the glass container
= 88 x 51
= 4488 cm
2 Height of water
= 89760 ÷ 4488
= 20 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment S
= 32 - 20
= 12 cm
Drop in the volume of Compartment S
= 51 x 40 x 12
= 24480 cm
3 Volume of water flowed from S to T in 1 minute
= 24480 ÷ 90
≈ 272.0 cm
3 Answer(s): (a) 20 cm; (b) 272.0 cm
3