This figure is not drawn to scale. A rectangular glass container 80 cm by 59 cm by 43 cm has 2 compartments, K and L, with a water height of 36 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
= 10 x 36 x 59
= 21240 cm
3 Length of Compartment L
= 80 - 10
= 70 cm
Volume of the water in Compartment L
= 70 x 59 x 12
= 49560 cm
3 Total volume of water
= 21240 + 49560
= 70800 cm
3 Base area of the glass container
= 80 x 59
= 4720 cm
2 Height of water
= 70800 ÷ 4720
= 15 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment K
= 36 - 15
= 21 cm
Drop in the volume of Compartment K
= 59 x 10 x 21
= 12390 cm
3 Volume of water flowed from K to L in 1 minute
= 12390 ÷ 75
≈ 165.2 cm
3 Answer(s): (a) 15 cm; (b) 165.2 cm
3