Question

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.
circumference = 7π feet, area = 49π square feet
circumference = 14π feet, area = 196π square feet
circumference = 14 feet, area = 14π square feet
circumference = 14π feet, area = 49π square feet

Explanation:

Step1: Recall formulas for circle

The formula for the circumference \( C \) of a circle with diameter \( d \) is \( C = \pi d \), and the formula for the area \( A \) of a circle with radius \( r \) is \( A=\pi r^{2} \), where \( r=\frac{d}{2} \).

Step2: Calculate circumference

Given the diameter \( d = 14 \) feet. Substitute into the circumference formula: \( C=\pi\times14 = 14\pi \) feet.

Step3: Calculate radius

The radius \( r=\frac{d}{2}=\frac{14}{2}=7 \) feet.

Step4: Calculate area

Substitute \( r = 7 \) into the area formula: \( A=\pi\times7^{2}=\pi\times49 = 49\pi \) square feet.

Answer:

circumference = \( 14\pi \) feet, area = \( 49\pi \) square feet (the fourth option in the list)