This figure is not drawn to scale. A rectangular glass tank 80 cm by 55 cm by 46 cm has 2 compartments, G and H, with a water height of 35 cm in G and 16 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 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 G to H in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment G
= 20 x 35 x 55
= 38500 cm
3 Length of Compartment H
= 80 - 20
= 60 cm
Volume of the water in Compartment H
= 60 x 55 x 16
= 52800 cm
3 Total volume of water
= 38500 + 52800
= 91300 cm
3 Base area of the glass tank
= 80 x 55
= 4400 cm
2 Height of water
= 91300 ÷ 4400
= 20.75 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment G
= 35 - 20.75
= 14.25 cm
Drop in the volume of Compartment G
= 55 x 20 x 14.25
= 15675 cm
3 Volume of water flowed from G to H in 1 minute
= 15675 ÷ 72
≈ 217.7 cm
3 Answer(s): (a) 20.75 cm; (b) 217.7 cm
3