This figure is not drawn to scale. A rectangular glass tank 75 cm by 52 cm by 47 cm has 2 compartments, R and S, with a water height of 34 cm in R and 14 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
= 33 x 34 x 52
= 58344 cm
3 Length of Compartment S
= 75 - 33
= 42 cm
Volume of the water in Compartment S
= 42 x 52 x 14
= 30576 cm
3 Total volume of water
= 58344 + 30576
= 88920 cm
3 Base area of the glass tank
= 75 x 52
= 3900 cm
2 Height of water
= 88920 ÷ 3900
= 22.8 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment R
= 34 - 22.8
= 11.2 cm
Drop in the volume of Compartment R
= 52 x 33 x 11.2
= 19219.2 cm
3 Volume of water flowed from R to S in 1 minute
= 19219.2 ÷ 75
≈ 256.3 cm
3 Answer(s): (a) 22.8 cm; (b) 256.3 cm
3