Circle
M
has a central angle,
∠LMN
, that measures
76°
. The radius of circle
M
is
3. 2
cm. Which is the area of the sector bounded by
∠LMN
to the nearest tenth of a square centimeter?
0:00 / 0:18
24. 4 cm
2
6. 8 cm
2
13. 6 cm
2
2. 2 cm
2


To find the area of a sector, we use the formula:

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

where:
- \(\theta\) is the central angle in degrees,
- \(r\) is the radius of the circle,
- \(\pi\) is a constant (approximately 3.14159).

### Given:
- Central angle (\(\theta\)) = 76°
- Radius (\(r\)) = 3.2 cm

### Calculating the area:
\[
\text{Area of sector} = \frac{76}{360} \times \pi \times (3.2)^2
\]

Let's compute it step-by-step:

1. Calculate \( (3.2)^2 \):
\[
(3.2)^2 = 10.24 \, \text{cm}^2
\]

2. Calculate \(\frac{76}{360}\):
\[
\frac{76}{360} \approx 0.2111
\]

3. Plug the values into the formula:
\[
\text{Area of sector} = 0.2111 \times \pi \times 10.24
\]

4. Multiply by \(\pi\) (using 3.14159):
\[
\text{Area of sector} = 0.2111 \times 3.14159 \times 10.24 \approx 6.8 \, \text{cm}^2
\]

### Answer:
The area of the sector is **6.8 cm²**, which matches the second option.

Would you like further details or have any questions? Here are 5 related questions for deeper understanding:

1. How is the formula for the area of a sector derived?
2. What is the circumference of the circle with the given radius?
3. How would the area change if the central angle was doubled?
4. What would be the area of the entire circle?
5. How do you convert an angle in degrees to radians?

**Tip:** Always double-check calculations, especially with rounding, to ensure accuracy in final answers.

Circle M has a central angle, ∠LMN, that measures 76°. The radius of circle M is 3.2 cm. What is the area of the sector bounded by ∠LMN to the nearest tenth of a square centimeter?

Learn how to calculate the area of a sector in a circle with a central angle of 76° and a radius of 3.2 cm. This step-by-step solution uses the formula for the area of a sector, providing detailed calculations suitable for Grades 7-9.

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