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What is the area of minor sector DFE?

To find the area of the minor sector \( \angle DFE \) in the circle, we can use the following formula:

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

where \( \theta \) is the central angle in degrees and \( r \) is the radius of the circle.

From the image:
- The central angle \( \theta = 100^\circ \)
- The radius \( r = 8.7 \) cm

Let's calculate the area of the minor sector \( DFE \):

\[ \text{Area of sector} = \frac{100^\circ}{360^\circ} \times \pi \times (8.7)^2 \]

Calculating this:

\[ \text{Area of sector} = \frac{100}{360} \times \pi \times 75.69 \]

\[ \text{Area of sector} = \frac{5}{18} \times \pi \times 75.69 \]

\[ \text{Area of sector} = \frac{5 \times 75.69}{18} \times \pi \]

\[ \text{Area of sector} \approx \frac{378.45}{18} \times \pi \]

\[ \text{Area of sector} \approx 21.025 \times \pi \]

\[ \text{Area of sector} \approx 66.05 \, \text{cm}^2 \]

Thus, the area of the minor sector \( DFE \) is approximately \( 66.05 \, \text{cm}^2 \).

Would you like more details or have any questions?

Here are 5 questions you might want to ask:
1. How do you calculate the area of a major sector?
2. How can you find the length of an arc in a sector?
3. What is the formula to find the area of a segment in a circle?
4. How can you find the radius of a circle if the area of a sector and its central angle are known?
5. What is the difference between radians and degrees in measuring angles?

**Tip:** Remember that the central angle of a sector and the radius of the circle are crucial for calculating both the area of the sector and the arc length. Always ensure your angle measurements are in the correct units (degrees or radians) for the formula you are using.

Learn how to calculate the area of minor sector DFE in a circle using the formula for sector area. This problem involves finding the area of a sector with a given central angle and radius. Suitable for high school students studying circle geometry and sector calculations.

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