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!