A gardener makes a new circular flower bed. The bed is fourteen feet in diameter. Calculate the circumference and the area of the circular flower bed.

A. Circumference [tex]$=14$[/tex] feet, Area [tex]$=14 \pi$[/tex] square feet
B. Circumference [tex]$=7 \pi$[/tex] feet, Area [tex]$=49 \pi$[/tex] square feet
C. Circumference [tex]$=14 \pi$[/tex] feet, Area [tex]$=196 \pi$[/tex] square feet
D. Circumference [tex]$=14 \pi$[/tex] feet, Area [tex]$=49 \pi$[/tex] square feet



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.