Question

find the circumference and the area of a circle with a radius of 4 in. the circumference is 25.1 in. (type an integer or decimal rounded to the nearest tenth as needed.) the area is (type an integer or decimal rounded to the nearest tenth as needed.)

Explanation:

Step1: Recall the formula for the area of a circle

The formula for the area \( A \) of a circle with radius \( r \) is \( A=\pi r^{2} \).

Step2: Substitute the given radius into the formula

Given that the radius \( r = 4 \) inches. Substitute \( r = 4 \) into the formula: \( A=\pi\times(4)^{2}=\pi\times16 \).

Step3: Calculate the numerical value

Using \( \pi\approx3.14159 \), we have \( A = 16\times3.14159\approx50.26544 \).

Step4: Round to the nearest tenth

Rounding \( 50.26544 \) to the nearest tenth gives \( 50.3 \).

Answer:

The area is \( 50.3 \) square inches.