The volume of a circular iron rod of length 1 m is `3850cm^(3)`. Find its diameter.

Answer

To find the diameter of a circular iron rod given its volume and length, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- Volume of the rod (V) = 3850 cm³
- Length of the rod (h) = 1 m = 100 cm (since 1 m = 100 cm)

2. **Use the Formula for the Volume of a Cylinder**:
The formula for the volume of a cylinder is:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height (or length) of the cylinder.

3. **Substitute the Known Values into the Formula**:
Substitute the values of volume and height into the formula:
\[ 3850 = \pi r^2 \times 100 \]

4. **Replace \(\pi\) with its Approximate Value**:
Use the value of \(\pi\) as \( \frac{22}{7} \):
\[ 3850 = \frac{22}{7} r^2 \times 100 \]

5. **Rearrange the Equation to Solve for \( r^2 \)**:
First, multiply both sides by \( \frac{7}{22} \) to isolate \( r^2 \):
\[ r^2 = \frac{3850 \times 7}{22 \times 100} \]

6. **Calculate the Right Side**:
- Calculate \( 3850 \times 7 = 26950 \)
- Calculate \( 22 \times 100 = 2200 \)
- Now, divide:
\[ r^2 = \frac{26950}{2200} = 12.25 \]

7. **Find the Radius \( r \)**:
Take the square root of both sides:
\[ r = \sqrt{12.25} = 3.5 \text{ cm} \]

8. **Calculate the Diameter \( d \)**:
The diameter \( d \) is twice the radius:
\[ d = 2r = 2 \times 3.5 = 7 \text{ cm} \]

### Final Answer:
The diameter of the circular iron rod is **7 cm**.

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