This figure is not drawn to scale. A rectangular glass container 70 cm by 53 cm by 48 cm has 2 compartments, K and L, with a water height of 34 cm in K and 18 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
= 28 x 34 x 53
= 50456 cm
3 Length of Compartment L
= 70 - 28
= 42 cm
Volume of the water in Compartment L
= 42 x 53 x 18
= 40068 cm
3 Total volume of water
= 50456 + 40068
= 90524 cm
3 Base area of the glass container
= 70 x 53
= 3710 cm
2 Height of water
= 90524 ÷ 3710
= 24.4 cm
(b)
1
15 h = 72 min
Drop in the height of Compartment K
= 34 - 24.4
= 9.6 cm
Drop in the volume of Compartment K
= 53 x 28 x 9.6
= 14246.4 cm
3 Volume of water flowed from K to L in 1 minute
= 14246.4 ÷ 72
≈ 197.9 cm
3 Answer(s): (a) 24.4 cm; (b) 197.9 cm
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