Question
3. The radius of a circle is 9 yards. \( \begin{array}{l} \text { a. What is the circumference of the circle? } \\ \)\[ \]\( =2 \pi r \\ c=2(3.14)(9) \\ c=56.52 \mathrm{yd}\end{array} \) b. What is the area of the circle?
Ask by Flynn French. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The area of the circle is approximately 254.34 square yards.
Solution
**Step 1: Recall the formula for the area of a circle.**
The area \( A \) is given by:
\[
A = \pi r^2
\]
**Step 2: Substitute the given radius.**
Given \( r = 9 \) yards, we substitute into the formula:
\[
A = \pi (9)^2 = \pi \times 81 = 81\pi
\]
**Step 3: Calculate the numerical value (if needed).**
Using \( \pi \approx 3.14 \):
\[
A \approx 81 \times 3.14 = 254.34 \text{ square yards}
\]
**Final Answer:**
The area of the circle is approximately \( 254.34 \) square yards.
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Simplify this solution Beyond the Answer
To find the area of a circle, you can use the formula \( A = \pi r^2 \). For your circle with a radius of 9 yards, that would be \( A = \pi (9)^2 = \pi (81) \), which approximately equals \( 254.34 \mathrm{yd}^2 \) when you use \( \pi \approx 3.14 \). Knowing these fundamentals of circles is not just academic; they play a huge role in various real-world applications! For example, engineers use the circumference when designing wheels, and artists calculate the area when planning the size of circular canvases or garden beds. Understanding the area and circumference can also assist in effective space planning in fields like landscaping and architecture.
