Find the angle at the centre of these sectors to the nearest degree.
a Area of 104.72 cm2 and a radius of 10 cm
b Area of 139.63 m2 and a radius of 40 m

To find the angle at the center of a sector, we use the formula for the area of a sector of a circle:

\[
A = \frac{\theta}{360} \times \pi r^2
\]

Where:
- \( A \) is the area of the sector
- \( \theta \) is the angle at the center (in degrees)
- \( r \) is the radius

Rearranging to solve for \( \theta \):

\[
\theta = \frac{A \times 360}{\pi r^2}
\]

### (a) For an area of 104.72 cm² and a radius of 10 cm:

\[
\theta = \frac{104.72 \times 360}{\pi \times 10^2}
\]

Let me calculate that.

### (b) For an area of 139.63 m² and a radius of 40 m:

\[
\theta = \frac{139.63 \times 360}{\pi \times 40^2}
\]

I will calculate both values now.The angles at the center of the sectors are:

(a) \( 120^\circ \) for an area of 104.72 cm² and a radius of 10 cm.
(b) \( 10^\circ \) for an area of 139.63 m² and a radius of 40 m.

Would you like more details or explanations on how these were derived? Here are five related questions:

1. How is the area of a full circle related to the area of a sector?
2. What are the units used when calculating sector areas and angles?
3. How can you convert degrees to radians in this context?
4. How does the radius impact the angle for a given area of a sector?
5. What happens to the angle if you double the radius of a sector with the same area?

**Tip:** When calculating angles or areas for sectors, always ensure that the units of the radius and area match to avoid errors.

Find the angle at the centre of these sectors to the nearest degree. a) Area of 104.72 cm² and a radius of 10 cm b) Area of 139.63 m² and a radius of 40 m.

Learn how to calculate the angle at the center of circle sectors with areas 104.72 cm² and 139.63 m² using the formula θ = (A × 360) / (π × r²). This solution includes detailed steps and covers key geometric concepts, suitable for students in Grades 9-12.

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