This figure is not drawn to scale. A rectangular glass tank 90 cm by 52 cm by 47 cm has 2 compartments, Q and R, with a water height of 37 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 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 Q to R in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Q
= 36 x 37 x 52
= 69264 cm
3 Length of Compartment R
= 90 - 36
= 54 cm
Volume of the water in Compartment R
= 54 x 52 x 12
= 33696 cm
3 Total volume of water
= 69264 + 33696
= 102960 cm
3 Base area of the glass tank
= 90 x 52
= 4680 cm
2 Height of water
= 102960 ÷ 4680
= 22 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment Q
= 37 - 22
= 15 cm
Drop in the volume of Compartment Q
= 52 x 36 x 15
= 28080 cm
3 Volume of water flowed from Q to R in 1 minute
= 28080 ÷ 90
≈ 312.0 cm
3 Answer(s): (a) 22 cm; (b) 312.0 cm
3