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 \\(16\pi\\) sq in. (simplify your answer. type an exact answer in terms of \\(\pi\\).) the approximate area is \\(\square\\) (simplify your answer. type a whole number, proper fraction, or a mixed number.) (circle image with \\(r = 4\\) in.)

Explanation:

Step1: Recall the area formula for a circle

The area of a circle is given by the formula \( A = \pi r^2 \). We know the radius \( r = 4 \) inches, and we are using \( \frac{22}{7} \) as an approximation for \( \pi \). First, we substitute \( r = 4 \) into the formula, so we have \( A = \frac{22}{7} \times 4^2 \).

Step2: Calculate \( 4^2 \)

\( 4^2 = 16 \), so now the formula becomes \( A = \frac{22}{7} \times 16 \).

Step3: Multiply the fractions

\( \frac{22}{7} \times 16=\frac{22\times16}{7}=\frac{352}{7} = 50\frac{2}{7} \) (or as a decimal, approximately 50.29, but we need to present it as a fraction or whole number/mixed number).

Answer:

\( 50\frac{2}{7} \) (or \( \frac{352}{7} \))