Find the area of the shaded sector of each circle. Leave your answer as a fraction in terms of pi , radius 20 and central age 74 degree

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

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

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

### Given:
- Central angle \(\theta = 74^\circ\),
- Radius \(r = 20\).

Now, substitute the given values into the formula:

\[
\text{Area of the sector} = \frac{74}{360} \times \pi \times 20^2
\]

Simplify the expression:

\[
\text{Area of the sector} = \frac{74}{360} \times \pi \times 400
\]

\[
\text{Area of the sector} = \frac{74 \times 400}{360} \times \pi
\]

\[
\text{Area of the sector} = \frac{29600}{360} \times \pi
\]

\[
\text{Area of the sector} = \frac{740}{9} \times \pi
\]

Thus, the area of the shaded sector is:

\[
\boxed{\frac{740}{9} \pi}
\]

Would you like further details or clarifications? 

Here are 5 related questions to explore:
1. How do you find the length of the arc for the same sector?
2. What would the area be if the central angle were doubled?
3. How does the area change if the radius is increased by 10 units?
4. Can you convert the fraction \(\frac{740}{9}\) to a decimal approximation?
5. How does the formula for sector area apply to radians instead of degrees?

**Tip:** Always keep track of the units you’re using for angle measurements (degrees or radians) in sector problems.

Find the area of the shaded sector of each circle. Leave your answer as a fraction in terms of pi, radius 20 and central angle 74 degrees.

Learn how to find the area of a shaded sector of a circle with radius 20 and central angle 74 degrees. This step-by-step solution uses the formula for the area of a sector, perfect for students in Grades 8-10. The answer is left as a fraction in terms of pi.

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