To find the circumference and area of a circular flower bed with a diameter of 14 feet, we need to follow these steps:
1. Calculate the radius of the circle:
The radius [tex]\( r \)[/tex] is half the diameter.
[tex]\[
r = \frac{\text{diameter}}{2} = \frac{14}{2} = 7 \text{ feet}
\][/tex]
2. Calculate the circumference:
The circumference [tex]\( C \)[/tex] of a circle can be calculated using the formula:
[tex]\[
C = \pi \times \text{diameter}
\][/tex]
In this case, the diameter is 14 feet, so:
[tex]\[
C = \pi \times 14 \approx 43.982297150257104 \text{ feet}
\][/tex]
3. Calculate the area:
The area [tex]\( A \)[/tex] of a circle can be calculated using the formula:
[tex]\[
A = \pi \times r^2
\][/tex]
Here, the radius [tex]\( r \)[/tex] is 7 feet, so:
[tex]\[
A = \pi \times (7^2) = \pi \times 49 \approx 153.93804002589985 \text{ square feet}
\][/tex]
Given the numerical results for the circumference and area, upon checking the provided multiple choice options, we see none of them match exactly with our results.
Nevertheless, viewing it through the theoretical formulas used for the circumference [tex]\( 14 \pi \)[/tex] feet and area [tex]\( 49 \pi \)[/tex] square feet aligns mathematically with the correct principles but using exact numerals of [tex]\( \pi \approx 3.14159 \)[/tex], we get real approximations:
- Approximate circumference: [tex]\( 43.982297150257104 \)[/tex] feet
- Approximate area: [tex]\( 153.93804002589985 \)[/tex] square feet
Hence, the proper matching theoretical answer case would be:
[tex]\[
\text{Circumference } = 14 \pi \text{ feet}, \quad \text{Area } = 49 \pi \text{ square feet}
\][/tex]
