This figure is not drawn to scale. A rectangular glass tank 75 cm by 55 cm by 42 cm has 2 compartments, R and S, with a water height of 40 cm in R and 12 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 tank 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
= 36 x 40 x 55
= 79200 cm
3 Length of Compartment S
= 75 - 36
= 39 cm
Volume of the water in Compartment S
= 39 x 55 x 12
= 25740 cm
3 Total volume of water
= 79200 + 25740
= 104940 cm
3 Base area of the glass tank
= 75 x 55
= 4125 cm
2 Height of water
= 104940 ÷ 4125
= 25.44 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment R
= 40 - 25.44
= 14.56 cm
Drop in the volume of Compartment R
= 55 x 36 x 14.56
= 28828.8 cm
3 Volume of water flowed from R to S in 1 minute
= 28828.8 ÷ 90
≈ 320.3 cm
3 Answer(s): (a) 25.44 cm; (b) 320.3 cm
3