Find the area of the sector of the circle shown below enclosed by Angle ACB.

Circle with radius 4 and central angle ACB measuring 115 degrees 

Enter your answer rounded to the nearest hundredth.

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

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

Where:
- \(\theta\) is the central angle in degrees,
- \(r\) is the radius of the circle.

Given:
- \(r = 4\),
- \(\theta = 115^\circ\).

Now, we can substitute the values into the formula:

\[
\text{Area of sector} = \frac{115^\circ}{360^\circ} \times \pi \times (4)^2
\]

Let's calculate this.import math

# Given values
radius = 4
angle_degrees = 115

# Area of sector formula
area_of_sector = (angle_degrees / 360) * math.pi * radius**2

# Round the result to the nearest hundredth
area_of_sector_rounded = round(area_of_sector, 2)
area_of_sector_roundedThe area of the sector enclosed by angle ACB is approximately **16.06** square units, rounded to the nearest hundredth.

Would you like more details or have any questions? Here are five related questions to expand on this topic:

1. How would the area change if the radius were doubled?
2. What happens to the sector's area if the angle is halved?
3. How do you find the length of the arc corresponding to the same sector?
4. Can you derive a formula for the area of a sector in terms of radians instead of degrees?
5. How does the area formula change for an elliptical sector?

**Tip:** Always check if the angle is in radians or degrees before applying formulas.

Learn how to calculate the area of a circle sector with a central angle of 115 degrees using the sector area formula. Given a circle with radius 4 units, find the area enclosed by the angle ACB. Detailed step-by-step solution provided.

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