This figure is not drawn to scale. A rectangular glass container 75 cm by 51 cm by 50 cm has 2 compartments, K and L, with a water height of 33 cm in K and 12 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 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 K to L in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment K
= 25 x 33 x 51
= 42075 cm
3 Length of Compartment L
= 75 - 25
= 50 cm
Volume of the water in Compartment L
= 50 x 51 x 12
= 30600 cm
3 Total volume of water
= 42075 + 30600
= 72675 cm
3 Base area of the glass container
= 75 x 51
= 3825 cm
2 Height of water
= 72675 ÷ 3825
= 19 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment K
= 33 - 19
= 14 cm
Drop in the volume of Compartment K
= 51 x 25 x 14
= 17850 cm
3 Volume of water flowed from K to L in 1 minute
= 17850 ÷ 75
≈ 238.0 cm
3 Answer(s): (a) 19 cm; (b) 238.0 cm
3