This figure is not drawn to scale. A rectangular glass tank 80 cm by 57 cm by 45 cm has 2 compartments, Q and R, with a water height of 39 cm in Q and 14 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 115 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
= 24 x 39 x 57
= 53352 cm
3 Length of Compartment R
= 80 - 24
= 56 cm
Volume of the water in Compartment R
= 56 x 57 x 14
= 44688 cm
3 Total volume of water
= 53352 + 44688
= 98040 cm
3 Base area of the glass tank
= 80 x 57
= 4560 cm
2 Height of water
= 98040 ÷ 4560
= 21.5 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment Q
= 39 - 21.5
= 17.5 cm
Drop in the volume of Compartment Q
= 57 x 24 x 17.5
= 23940 cm
3 Volume of water flowed from Q to R in 1 minute
= 23940 ÷ 72
≈ 332.5 cm
3 Answer(s): (a) 21.5 cm; (b) 332.5 cm
3