This figure is not drawn to scale. A rectangular glass container 76 cm by 57 cm by 44 cm has 2 compartments, K and L, with a water height of 36 cm in K and 17 cm in L. A hole in the slider caused water to leak from K to L. 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 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 K to L in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment K
= 33 x 36 x 57
= 67716 cm
3 Length of Compartment L
= 76 - 33
= 43 cm
Volume of the water in Compartment L
= 43 x 57 x 17
= 41667 cm
3 Total volume of water
= 67716 + 41667
= 109383 cm
3 Base area of the glass container
= 76 x 57
= 4332 cm
2 Height of water
= 109383 ÷ 4332
= 25.25 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment K
= 36 - 25.25
= 10.75 cm
Drop in the volume of Compartment K
= 57 x 33 x 10.75
= 20220.75 cm
3 Volume of water flowed from K to L in 1 minute
= 20220.75 ÷ 105
≈ 192.6 cm
3 Answer(s): (a) 25.25 cm; (b) 192.6 cm
3