This exercise involves the formula for the area of a circular sector.

A sector of a circle has a central angle of 145°. Find the area of the sector if the radius of the circle is 8 ft. (Round your answer to one decimal place.)
 ft2

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

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

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

Given:
- \(\theta = 145^\circ\)
- \(r = 8\) ft

Let's calculate the area of the sector.

\[
\text{Area} = \frac{145^\circ}{360^\circ} \times \pi \times (8)^2
\]

\[
\text{Area} = \frac{145^\circ}{360^\circ} \times \pi \times 64
\]

\[
\text{Area} = \frac{145}{360} \times 64\pi
\]

\[
\text{Area} \approx 0.4028 \times 201.06
\]

\[
\text{Area} \approx 81.0 \, \text{ft}^2
\]

So, the area of the sector is approximately **81.0 square feet**.

Would you like further details on this calculation or have any other questions?

---

Here are 5 related questions you might consider:
1. What is the area of a sector with a 90° central angle and a radius of 10 ft?
2. How would the area change if the central angle were doubled?
3. What is the area of a full circle with the same radius of 8 ft?
4. How do you convert radians to degrees in the context of sector area calculations?
5. What happens to the sector's area if the radius is halved?

**Tip:** When dealing with sector areas, ensure the angle is always in degrees (or convert to degrees) before using the standard sector area formula.

A sector of a circle has a central angle of 145°. Find the area of the sector if the radius of the circle is 8 ft. (Round your answer to one decimal place.)

Learn how to calculate the area of a sector of a circle with a 145° central angle and a radius of 8 ft. This problem involves the application of the area of a sector formula. Get a detailed step-by-step solution and round your answer to one decimal place.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation