Answer :
To solve the problem of finding the circumference and area of a circular flower bed with a diameter of 14 feet, we need to use the formulas for the circumference and the area of a circle.
### Step-by-Step Solution:
1. Diameter and Radius:
The diameter of the flower bed is given as 14 feet. The radius (\( r \)) of the circle is half of the diameter.
[tex]\[ r = \frac{d}{2} = \frac{14}{2} = 7 \text{ feet} \][/tex]
2. Circumference:
The formula for the circumference (\( C \)) of a circle is:
[tex]\[ C = 2\pi r \][/tex]
Substituting the radius:
[tex]\[ C = 2\pi \times 7 = 14\pi \text{ feet} \][/tex]
3. Area:
The formula for the area (\( A \)) of a circle is:
[tex]\[ A = \pi r^2 \][/tex]
Substituting the radius:
[tex]\[ A = \pi \times 7^2 = \pi \times 49 = 49\pi \text{ square feet} \][/tex]
In conclusion:
The circumference of the circular flower bed is \( 14\pi \) feet, and the area is \( 49\pi \) square feet.
So, the correct answer is:
Circumference \( = 14\pi \) feet, area \( = 49\pi \) square feet.
Examining the provided options, the correct one is:
- circumference [tex]\( = 14\pi \)[/tex] feet, area [tex]\( = 49\pi \)[/tex] square feet.
### Step-by-Step Solution:
1. Diameter and Radius:
The diameter of the flower bed is given as 14 feet. The radius (\( r \)) of the circle is half of the diameter.
[tex]\[ r = \frac{d}{2} = \frac{14}{2} = 7 \text{ feet} \][/tex]
2. Circumference:
The formula for the circumference (\( C \)) of a circle is:
[tex]\[ C = 2\pi r \][/tex]
Substituting the radius:
[tex]\[ C = 2\pi \times 7 = 14\pi \text{ feet} \][/tex]
3. Area:
The formula for the area (\( A \)) of a circle is:
[tex]\[ A = \pi r^2 \][/tex]
Substituting the radius:
[tex]\[ A = \pi \times 7^2 = \pi \times 49 = 49\pi \text{ square feet} \][/tex]
In conclusion:
The circumference of the circular flower bed is \( 14\pi \) feet, and the area is \( 49\pi \) square feet.
So, the correct answer is:
Circumference \( = 14\pi \) feet, area \( = 49\pi \) square feet.
Examining the provided options, the correct one is:
- circumference [tex]\( = 14\pi \)[/tex] feet, area [tex]\( = 49\pi \)[/tex] square feet.
