This figure is not drawn to scale. A rectangular glass container 75 cm by 51 cm by 48 cm has 2 compartments, K and L, with a water height of 33 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 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
= 12 x 33 x 51
= 20196 cm
3 Length of Compartment L
= 75 - 12
= 63 cm
Volume of the water in Compartment L
= 63 x 51 x 17
= 54621 cm
3 Total volume of water
= 20196 + 54621
= 74817 cm
3 Base area of the glass container
= 75 x 51
= 3825 cm
2 Height of water
= 74817 ÷ 3825
= 19.56 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment K
= 33 - 19.56
= 13.44 cm
Drop in the volume of Compartment K
= 51 x 12 x 13.44
= 8225.28 cm
3 Volume of water flowed from K to L in 1 minute
= 8225.28 ÷ 75
≈ 109.7 cm
3 Answer(s): (a) 19.56 cm; (b) 109.7 cm
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