This figure is not drawn to scale. A rectangular glass tank 75 cm by 56 cm by 44 cm has 2 compartments, L and M, with a water height of 39 cm in L and 10 cm in M. A hole in the slider caused water to leak from L to M. 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 L to M in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment L
= 24 x 39 x 56
= 52416 cm
3 Length of Compartment M
= 75 - 24
= 51 cm
Volume of the water in Compartment M
= 51 x 56 x 10
= 28560 cm
3 Total volume of water
= 52416 + 28560
= 80976 cm
3 Base area of the glass tank
= 75 x 56
= 4200 cm
2 Height of water
= 80976 ÷ 4200
= 19.28 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment L
= 39 - 19.28
= 19.72 cm
Drop in the volume of Compartment L
= 56 x 24 x 19.72
= 26503.68 cm
3 Volume of water flowed from L to M in 1 minute
= 26503.68 ÷ 105
≈ 252.4 cm
3 Answer(s): (a) 19.28 cm; (b) 252.4 cm
3