This figure is not drawn to scale. A rectangular glass tank 90 cm by 51 cm by 41 cm has 2 compartments, F and G, with a water height of 33 cm in F and 15 cm in G. A hole in the slider caused water to leak from F to G. 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 F to G in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment F
= 20 x 33 x 51
= 33660 cm
3 Length of Compartment G
= 90 - 20
= 70 cm
Volume of the water in Compartment G
= 70 x 51 x 15
= 53550 cm
3 Total volume of water
= 33660 + 53550
= 87210 cm
3 Base area of the glass tank
= 90 x 51
= 4590 cm
2 Height of water
= 87210 ÷ 4590
= 19 cm
(b)
1
12 h = 90 min
Drop in the height of Compartment F
= 33 - 19
= 14 cm
Drop in the volume of Compartment F
= 51 x 20 x 14
= 14280 cm
3 Volume of water flowed from F to G in 1 minute
= 14280 ÷ 90
≈ 158.7 cm
3 Answer(s): (a) 19 cm; (b) 158.7 cm
3