Question

find the circumference and the area of a circle with a radius of 3 in. the circumference is (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Recall the formula for circumference of a circle

The formula for the circumference \( C \) of a circle is \( C = 2\pi r \), where \( r \) is the radius.
Given \( r = 3 \) in, substitute into the formula: \( C = 2\times\pi\times3 \)

Step2: Calculate the circumference

\( C = 6\pi \approx 6\times3.1416 \approx 18.8 \) (rounded to the nearest tenth)

Step3: Recall the formula for area of a circle

The formula for the area \( A \) of a circle is \( A=\pi r^{2} \)
Given \( r = 3 \) in, substitute into the formula: \( A=\pi\times3^{2}=\pi\times9 \)

Step4: Calculate the area

\( A = 9\pi\approx9\times3.1416\approx28.3 \) (rounded to the nearest tenth)

Answer:

The circumference is approximately \( 18.8 \) inches and the area is approximately \( 28.3 \) square inches.