This figure is not drawn to scale. A rectangular glass tank 78 cm by 57 cm by 50 cm has 2 compartments, Q and R, with a water height of 40 cm in Q and 12 cm in R. A hole in the slider caused water to leak from Q to R. 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 134 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 Q to R in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Q
= 39 x 40 x 57
= 88920 cm
3 Length of Compartment R
= 78 - 39
= 39 cm
Volume of the water in Compartment R
= 39 x 57 x 12
= 26676 cm
3 Total volume of water
= 88920 + 26676
= 115596 cm
3 Base area of the glass tank
= 78 x 57
= 4446 cm
2 Height of water
= 115596 ÷ 4446
= 26 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment Q
= 40 - 26
= 14 cm
Drop in the volume of Compartment Q
= 57 x 39 x 14
= 31122 cm
3 Volume of water flowed from Q to R in 1 minute
= 31122 ÷ 105
≈ 296.4 cm
3 Answer(s): (a) 26 cm; (b) 296.4 cm
3