Question

find the area of the given geometric figure. if the figure is a circle, give an exact area and then use \\(\frac{22}{7}\\) as an approximation for \\(\pi\\) to approximate the area. the exact area of the circle is \\(\square\\) (simplify your answer. type an exact answer in terms of \\(\pi\\).) (note: the image shows a circle with radius \\(r = 4\\) in.)

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

We are given that the radius \( r = 4 \) inches. Substituting \( r = 4 \) into the formula \( A=\pi r^{2} \), we get \( A=\pi\times(4)^{2} \).

Step3: Simplify the expression

Calculating \( (4)^{2}=16 \), so the area \( A = 16\pi \) square inches.

Answer:

\( 16\pi \) square inches (or \( 16\pi \) in²)