This figure is not drawn to scale. A rectangular glass tank 88 cm by 51 cm by 41 cm has 2 compartments, L and M, with a water height of 31 cm in L and 20 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 114 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
= 40 x 31 x 51
= 63240 cm
3 Length of Compartment M
= 88 - 40
= 48 cm
Volume of the water in Compartment M
= 48 x 51 x 20
= 48960 cm
3 Total volume of water
= 63240 + 48960
= 112200 cm
3 Base area of the glass tank
= 88 x 51
= 4488 cm
2 Height of water
= 112200 ÷ 4488
= 25 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment L
= 31 - 25
= 6 cm
Drop in the volume of Compartment L
= 51 x 40 x 6
= 12240 cm
3 Volume of water flowed from L to M in 1 minute
= 12240 ÷ 75
≈ 163.2 cm
3 Answer(s): (a) 25 cm; (b) 163.2 cm
3