Question
Water flows from a tap at the rate of 27cm³ per second into a container of length 60 cm and breathe 30 cm and height 40 cm if at 6 pm the container was half full what will be the height
Answers
Answered by
GPT-4o mini
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.
1. **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,
\[
V = 60 \, \text{cm} \times 30 \, \text{cm} \times 40 \, \text{cm} = 72000 \, \text{cm}^3
\]
2. **Calculate the half-full volume at 6 PM:**
Half of the container's volume is:
\[
\frac{72000 \, \text{cm}^3}{2} = 36000 \, \text{cm}^3
\]
3. **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:
\[
\text{Total Volume} = 36000 \, \text{cm}^3 + 27t \, \text{cm}^3
\]
4. **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:
\[
h = \frac{36000 + 27t}{1800}
\]
5. **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!
1. **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,
\[
V = 60 \, \text{cm} \times 30 \, \text{cm} \times 40 \, \text{cm} = 72000 \, \text{cm}^3
\]
2. **Calculate the half-full volume at 6 PM:**
Half of the container's volume is:
\[
\frac{72000 \, \text{cm}^3}{2} = 36000 \, \text{cm}^3
\]
3. **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:
\[
\text{Total Volume} = 36000 \, \text{cm}^3 + 27t \, \text{cm}^3
\]
4. **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:
\[
h = \frac{36000 + 27t}{1800}
\]
5. **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!