To solve this problem, we'll follow the steps to calculate the circumference and area of a circular flower bed, given its diameter.
### Step 1: Understand the Problem
The diameter of the flower bed is given as 14 feet. We need to calculate:
- The circumference of the circle.
- The area of the circle.
### Step 2: Recall the Formulas
For a circle:
- The radius [tex]\( r \)[/tex] is half of the diameter.
- The circumference [tex]\( C \)[/tex] is given by [tex]\( C = 2\pi r \)[/tex].
- The area [tex]\( A \)[/tex] is given by [tex]\( A = \pi r^2 \)[/tex].
### Step 3: Calculate the Radius
Given the diameter [tex]\( d = 14 \)[/tex] feet, the radius [tex]\( r \)[/tex] is:
[tex]\[ r = \frac{d}{2} = \frac{14}{2} = 7 \text{ feet} \][/tex]
### Step 4: Calculate the Circumference
Using the formula for circumference:
[tex]\[ C = 2\pi r = 2\pi \times 7 = 14\pi \text{ feet} \][/tex]
### Step 5: Calculate the Area
Using the formula for area:
[tex]\[ A = \pi r^2 = \pi \times 7^2 = \pi \times 49 = 49\pi \text{ square feet} \][/tex]
### Step 6: Verify the Results
- The circumference is [tex]\( 14\pi \)[/tex] feet.
- The area is [tex]\( 49\pi \)[/tex] square feet.
### Step 7: Choose the Correct Answer
Comparing with the given options:
- Circumference [tex]\( = 14\pi \)[/tex] feet
- Area [tex]\( = 49\pi \)[/tex] square feet
Thus, the correct choice is:
[tex]\[
\boxed{\text{circumference } = 14\pi \text{ feet, area } = 49\pi \text{ square feet}}
\][/tex]
