This figure is not drawn to scale. A rectangular glass container 80 cm by 55 cm by 49 cm has 2 compartments, R and S, with a water height of 36 cm in R and 16 cm in S. A hole in the slider caused water to leak from R to S. 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 R to S in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment R
= 29 x 36 x 55
= 57420 cm
3 Length of Compartment S
= 80 - 29
= 51 cm
Volume of the water in Compartment S
= 51 x 55 x 16
= 44880 cm
3 Total volume of water
= 57420 + 44880
= 102300 cm
3 Base area of the glass container
= 80 x 55
= 4400 cm
2 Height of water
= 102300 ÷ 4400
= 23.25 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment R
= 36 - 23.25
= 12.75 cm
Drop in the volume of Compartment R
= 55 x 29 x 12.75
= 20336.25 cm
3 Volume of water flowed from R to S in 1 minute
= 20336.25 ÷ 90
≈ 226 cm
3 Answer(s): (a) 23.25 cm; (b) 226 cm
3