This figure is not drawn to scale. A rectangular glass container 90 cm by 50 cm by 50 cm has 2 compartments, K and L, with a water height of 30 cm in K and 15 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
= 27 x 30 x 50
= 40500 cm
3 Length of Compartment L
= 90 - 27
= 63 cm
Volume of the water in Compartment L
= 63 x 50 x 15
= 47250 cm
3 Total volume of water
= 40500 + 47250
= 87750 cm
3 Base area of the glass container
= 90 x 50
= 4500 cm
2 Height of water
= 87750 ÷ 4500
= 19.5 cm
(b)
1
34 h = 105 min
Drop in the height of Compartment K
= 30 - 19.5
= 10.5 cm
Drop in the volume of Compartment K
= 50 x 27 x 10.5
= 14175 cm
3 Volume of water flowed from K to L in 1 minute
= 14175 ÷ 105
≈ 135.0 cm
3 Answer(s): (a) 19.5 cm; (b) 135.0 cm
3