This figure is not drawn to scale. A rectangular glass tank 75 cm by 54 cm by 47 cm has 2 compartments, G and H, with a water height of 30 cm in G and 17 cm in H. A hole in the slider caused water to leak from G to H. 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 G to H in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment G
= 21 x 30 x 54
= 34020 cm
3 Length of Compartment H
= 75 - 21
= 54 cm
Volume of the water in Compartment H
= 54 x 54 x 17
= 49572 cm
3 Total volume of water
= 34020 + 49572
= 83592 cm
3 Base area of the glass tank
= 75 x 54
= 4050 cm
2 Height of water
= 83592 ÷ 4050
= 20.64 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment G
= 30 - 20.64
= 9.36 cm
Drop in the volume of Compartment G
= 54 x 21 x 9.36
= 10614.24 cm
3 Volume of water flowed from G to H in 1 minute
= 10614.24 ÷ 90
≈ 117.9 cm
3 Answer(s): (a) 20.64 cm; (b) 117.9 cm
3