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To solve the problem, we need to calculate the area of sector **OAB**, which is a major sector of a circle. Here’s the breakdown of the steps:

### Step 1: Calculate the total area of the circle
The formula for the area of a circle is:

\[
A = \pi r^2
\]

Where:
- \(r\) is the radius of the circle, which is 32 mm.

\[
A = \pi (32)^2 = \pi \times 1024 \approx 3216.99 \, \text{mm}^2
\]

### Step 2: Determine the angle of the major sector
Since **OAB** is a **major sector**, the angle for this sector is the complement of the given angle. The given angle for the minor sector is \(61^\circ\), so the angle for the major sector is:

\[
\theta_{\text{major}} = 360^\circ - 61^\circ = 299^\circ
\]

### Step 3: Use the formula for the area of a sector
The area of a sector is calculated by the formula:

\[
\text{Area of sector} = \frac{\theta}{360^\circ} \times \pi r^2
\]

Where:
- \(\theta = 299^\circ\) (the angle of the major sector)
- \(r = 32 \, \text{mm}\)

Substituting the values:

\[
\text{Area of sector OAB} = \frac{299}{360} \times 3216.99 \, \text{mm}^2
\]

\[
\text{Area of sector OAB} \approx 2672.08 \, \text{mm}^2
\]

### Final Answer:
The area of sector **OAB** is approximately \(2672.1 \, \text{mm}^2\) to 1 decimal place.

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Do you want more details or have any questions?

### Related Questions:
1. What is the area of the minor sector of the circle?
2. How do we calculate the arc length of the major sector?
3. Can you explain why we subtract the angle from 360° for the major sector?
4. How would the result change if the radius were doubled?
5. What would happen if both sectors were the same size (i.e., angle of 180°)?

**Tip**: Always double-check whether the sector is "major" or "minor," as this affects the angle used in calculations!

Calculate the area of the major sector OAB in a circle where the radius is 32 mm and the angle of the minor sector is 61°. Give your answer in mm² to 1 decimal place.

Learn how to calculate the area of a major sector in a circle with a radius of 32 mm and an angle of 61°. This problem uses the area of a circle formula and the sector area calculation formula. Suitable for students in Grades 8-10.

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