A sector with a central angle measure of
[\purpleD{200\degree}] has a radius of
[\maroonD{9,\text{cm}}].What is the area of the sector in terms of pie?

To express the area of the sector in terms of \(\pi\), you can use the formula:

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

Given:
\[
\theta = 200^\circ, \quad r = 9\,\text{cm}
\]

Substitute the values into the formula:

\[
\text{Area of the sector} = \frac{200^\circ}{360^\circ} \times \pi \times (9\,\text{cm})^2
\]

Simplify the fraction:

\[
\frac{200^\circ}{360^\circ} = \frac{5}{9}
\]

Now, calculate the area:

\[
\text{Area of the sector} = \frac{5}{9} \times \pi \times 81\,\text{cm}^2
\]

\[
\text{Area of the sector} = \frac{405\pi}{9}\,\text{cm}^2 = 45\pi\,\text{cm}^2
\]

Thus, the area of the sector in terms of \(\pi\) is:

\[
\boxed{45\pi\,\text{cm}^2}
\]

Would you like more details or have any questions?

Here are some related questions:
1. How does the central angle affect the sector's area in terms of \(\pi\)?
2. What would be the area of the sector if the central angle were \(100^\circ\)?
3. How do you calculate the length of the arc of the sector?
4. How does the radius affect the area of the sector in terms of \(\pi\)?
5. Can you express the area of a full circle in terms of \(\pi\) using the given radius?

**Tip:** Keep the final answer in terms of \(\pi\) unless asked for a numerical approximation. This keeps your result exact and often simplifies further calculations.

Discover how to calculate the area of a sector with a central angle of 200 degrees using the formula A = (theta / 360 degrees) * pi * r^2. Follow a step-by-step solution with detailed calculations and understand the impact of angle and radius on sector area. Suitable for Grades 9-12 students.

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