This figure is not drawn to scale. A rectangular glass container 88 cm by 56 cm by 48 cm has 2 compartments, L and M, with a water height of 35 cm in L and 13 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 container 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
= 36 x 35 x 56
= 70560 cm
3 Length of Compartment M
= 88 - 36
= 52 cm
Volume of the water in Compartment M
= 52 x 56 x 13
= 37856 cm
3 Total volume of water
= 70560 + 37856
= 108416 cm
3 Base area of the glass container
= 88 x 56
= 4928 cm
2 Height of water
= 108416 ÷ 4928
= 22 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment L
= 35 - 22
= 13 cm
Drop in the volume of Compartment L
= 56 x 36 x 13
= 26208 cm
3 Volume of water flowed from L to M in 1 minute
= 26208 ÷ 75
≈ 349.4 cm
3 Answer(s): (a) 22 cm; (b) 349.4 cm
3