This figure is not drawn to scale. A rectangular glass container 75 cm by 51 cm by 43 cm has 2 compartments, F and G, with a water height of 40 cm in F and 13 cm in G. A hole in the slider caused water to leak from F to G. 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 F to G in 1 minute? Express your answer to 1 decimal place in cm³.
(a)
Volume of water in Compartment F
= 32 x 40 x 51
= 65280 cm
3 Length of Compartment G
= 75 - 32
= 43 cm
Volume of the water in Compartment G
= 43 x 51 x 13
= 28509 cm
3 Total volume of water
= 65280 + 28509
= 93789 cm
3 Base area of the glass container
= 75 x 51
= 3825 cm
2 Height of water
= 93789 ÷ 3825
= 24.52 cm
(b)
1
14 h = 75 min
Drop in the height of Compartment F
= 40 - 24.52
= 15.48 cm
Drop in the volume of Compartment F
= 51 x 32 x 15.48
= 25263.36 cm
3 Volume of water flowed from F to G in 1 minute
= 25263.36 ÷ 75
≈ 336.8 cm
3 Answer(s): (a) 24.52 cm; (b) 336.8 cm
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