This figure is not drawn to scale. A rectangular glass tank 90 cm by 56 cm by 43 cm has 2 compartments, G and H, with a water height of 36 cm in G and 18 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 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 G to H in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment G
= 17 x 36 x 56
= 34272 cm
3 Length of Compartment H
= 90 - 17
= 73 cm
Volume of the water in Compartment H
= 73 x 56 x 18
= 73584 cm
3 Total volume of water
= 34272 + 73584
= 107856 cm
3 Base area of the glass tank
= 90 x 56
= 5040 cm
2 Height of water
= 107856 ÷ 5040
= 21.4 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment G
= 36 - 21.4
= 14.6 cm
Drop in the volume of Compartment G
= 56 x 17 x 14.6
= 13899.2 cm
3 Volume of water flowed from G to H in 1 minute
= 13899.2 ÷ 105
≈ 132.4 cm
3 Answer(s): (a) 21.4 cm; (b) 132.4 cm
3