This figure is not drawn to scale. A rectangular glass tank 80 cm by 51 cm by 45 cm has 2 compartments, F and G, with a water height of 34 cm in F and 10 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 134 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
= 15 x 34 x 51
= 26010 cm
3 Length of Compartment G
= 80 - 15
= 65 cm
Volume of the water in Compartment G
= 65 x 51 x 10
= 33150 cm
3 Total volume of water
= 26010 + 33150
= 59160 cm
3 Base area of the glass tank
= 80 x 51
= 4080 cm
2 Height of water
= 59160 ÷ 4080
= 14.5 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment F
= 34 - 14.5
= 19.5 cm
Drop in the volume of Compartment F
= 51 x 15 x 19.5
= 14917.5 cm
3 Volume of water flowed from F to G in 1 minute
= 14917.5 ÷ 105
≈ 142.1 cm
3 Answer(s): (a) 14.5 cm; (b) 142.1 cm
3