To determine the height of water in the container at a given time, we need to first calculate how much water is being added to the container from 6 PM on.
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Determine the volume of the container: The volume \( V \) of the container is given by the formula: \[ V = \text{length} \times \text{breadth} \times \text{height} \] Given the dimensions of the container:
- Length = 60 cm
- Breadth = 30 cm
- Height = 40 cm
So, \[ V = 60 , \text{cm} \times 30 , \text{cm} \times 40 , \text{cm} = 72000 , \text{cm}^3 \]
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Calculate the half-full volume at 6 PM: Half of the container's volume is: \[ \frac{72000 , \text{cm}^3}{2} = 36000 , \text{cm}^3 \]
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Calculate how much water is added after 6 PM: To find out how much water is added after 6 PM, we need to know the duration and the rate at which water flows in.
- Assume we need to calculate the height at a certain time (let's say \( t \) seconds after 6 PM).
The flow rate is 27 cm³ per second. After \( t \) seconds, the volume of water added is: \[ \text{Volume added} = 27 , \text{cm}^3/\text{sec} \times t \]
Therefore, the total volume in the container after \( t \) seconds would be: \[ \text{Total Volume} = 36000 , \text{cm}^3 + 27t , \text{cm}^3 \]
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Convert total volume back to height: To find the height of the water in the container, we can use the volume to height conversion, using the base area of the container. The base area \( A \) is: \[ A = \text{length} \times \text{breadth} = 60 , \text{cm} \times 30 , \text{cm} = 1800 , \text{cm}^2 \]
The height \( h \) corresponding to a volume \( V \) can be given by: \[ h = \frac{V}{A} \]
Substituting the total volume we have: \[ h = \frac{36000 + 27t}{1800} \]
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Evaluate the height based on the time elapsed: If you have a specific time (in seconds) after 6 PM when you want to know the height, just plug \( t \) (time in seconds) into the equation above to find the height.
Let me know if you have a specific time in mind for \( t \), and I can calculate the height for that!