This figure is not drawn to scale. A rectangular glass tank 84 cm by 53 cm by 45 cm has 2 compartments, Q and R, with a water height of 38 cm in Q and 17 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 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 Q to R in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment Q
= 26 x 38 x 53
= 52364 cm
3 Length of Compartment R
= 84 - 26
= 58 cm
Volume of the water in Compartment R
= 58 x 53 x 17
= 52258 cm
3 Total volume of water
= 52364 + 52258
= 104622 cm
3 Base area of the glass tank
= 84 x 53
= 4452 cm
2 Height of water
= 104622 ÷ 4452
= 23.5 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment Q
= 38 - 23.5
= 14.5 cm
Drop in the volume of Compartment Q
= 53 x 26 x 14.5
= 19981 cm
3 Volume of water flowed from Q to R in 1 minute
= 19981 ÷ 75
≈ 266.4 cm
3 Answer(s): (a) 23.5 cm; (b) 266.4 cm
3