This figure is not drawn to scale. A rectangular glass tank 75 cm by 59 cm by 41 cm has 2 compartments, R and S, with a water height of 31 cm in R and 10 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 114 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
= 13 x 31 x 59
= 23777 cm
3 Length of Compartment S
= 75 - 13
= 62 cm
Volume of the water in Compartment S
= 62 x 59 x 10
= 36580 cm
3 Total volume of water
= 23777 + 36580
= 60357 cm
3 Base area of the glass tank
= 75 x 59
= 4425 cm
2 Height of water
= 60357 ÷ 4425
= 13.64 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment R
= 31 - 13.64
= 17.36 cm
Drop in the volume of Compartment R
= 59 x 13 x 17.36
= 13315.12 cm
3 Volume of water flowed from R to S in 1 minute
= 13315.12 ÷ 75
≈ 177.5 cm
3 Answer(s): (a) 13.64 cm; (b) 177.5 cm
3