This figure is not drawn to scale. A rectangular glass container 84 cm by 54 cm by 42 cm has 2 compartments, K and L, with a water height of 34 cm in K and 13 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 115 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
= 14 x 34 x 54
= 25704 cm
3 Length of Compartment L
= 84 - 14
= 70 cm
Volume of the water in Compartment L
= 70 x 54 x 13
= 49140 cm
3 Total volume of water
= 25704 + 49140
= 74844 cm
3 Base area of the glass container
= 84 x 54
= 4536 cm
2 Height of water
= 74844 ÷ 4536
= 16.5 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment K
= 34 - 16.5
= 17.5 cm
Drop in the volume of Compartment K
= 54 x 14 x 17.5
= 13230 cm
3 Volume of water flowed from K to L in 1 minute
= 13230 ÷ 72
≈ 183.8 cm
3 Answer(s): (a) 16.5 cm; (b) 183.8 cm
3