The volume of a conical tent is `1232 m ^(3)` and the area of the base floor is `154 m^(2).` Calculate the :
radius of the floor,

Answer

To find the radius of the floor of the conical tent, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Problem**: We are given the volume of a conical tent as \(1232 \, m^3\) and the area of the base floor as \(154 \, m^2\). We need to find the radius of the base of the cone.

2. **Formula for Area of Circle**: The area \(A\) of the base of the cone, which is circular, is given by the formula:
\[ A = \pi r^2 \]
where \(r\) is the radius of the base.

3. **Substituting the Given Area**: We know the area of the base is \(154 \, m^2\). Therefore, we can set up the equation:
\[ \pi r^2 = 154 \]

4. **Using Approximate Value of \(\pi\)**: For calculations, we can use \(\pi \approx \frac{22}{7}\). Substituting this value into the equation gives:
\[ \frac{22}{7} r^2 = 154 \]

5. **Eliminating the Fraction**: To eliminate the fraction, multiply both sides of the equation by \(7\):
\[ 22 r^2 = 154 \times 7 \]

6. **Calculating \(154 \times 7\)**: Now, calculate \(154 \times 7\):
\[ 154 \times 7 = 1078 \]
So, we have:
\[ 22 r^2 = 1078 \]

7. **Isolating \(r^2\)**: Next, divide both sides by \(22\) to solve for \(r^2\):
\[ r^2 = \frac{1078}{22} \]

8. **Calculating \(\frac{1078}{22}\)**: Now, perform the division:
\[ r^2 = 49 \]

9. **Finding the Radius \(r\)**: Finally, take the square root of both sides to find \(r\):
\[ r = \sqrt{49} = 7 \]

10. **Final Answer**: Therefore, the radius of the floor of the conical tent is:
\[ r = 7 \, m \]