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We are given that an arc has a length of 4.75 cm and subtends an angle of 0.91 radians. We need to determine the diameter and circumference of the circle.

### Step 1: Use the arc length formula
The formula for the arc length \( s \) of a circle is:
\[
s = r \theta
\]
where:
- \( s \) is the arc length,
- \( r \) is the radius of the circle,
- \( \theta \) is the angle in radians.

We are given:
\[
s = 4.75 \, \text{cm}, \quad \theta = 0.91 \, \text{radians}
\]
We can rearrange this formula to solve for \( r \):
\[
r = \frac{s}{\theta} = \frac{4.75}{0.91}
\]

### Step 2: Calculate the radius
Let me calculate the radius.It seems like I can’t do more advanced data analysis right now. Please try again later.

If you'd like, you can calculate the radius manually using the formula:
\[
r = \frac{4.75}{0.91} \approx 5.22 \, \text{cm}
\]
Now, using this radius, you can calculate the diameter and circumference.

1. **Diameter**: 
\[
\text{Diameter} = 2r = 2 \times 5.22 \, \text{cm} = 10.44 \, \text{cm}
\]

2. **Circumference**: 
\[
\text{Circumference} = 2 \pi r = 2 \pi \times 5.22 \approx 32.79 \, \text{cm}
\]

Would you like further details or have any other questions?

Here are some related questions:
1. How is the arc length formula derived?
2. What is the difference between radians and degrees?
3. How does the value of \( \pi \) affect calculations in geometry?
4. How do you convert an angle in degrees to radians?
5. What are practical applications of arc length in real life?

**Tip:** Always make sure that the angle is in radians when using the arc length formula, as this is a common source of mistakes!

Determine the diameter and circumference of a circle if an arc of length 4.75 cm subtends an angle of 0.91 radians.

Learn how to calculate the diameter and circumference of a circle when given an arc length of 4.75 cm and a subtended angle of 0.91 radians. This problem involves the use of the arc length formula and the concepts of radians and circle geometry.

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