Question

find the area of the circle. given the exact area and then use the approximation 3.14 for π to approximate the area. the exact area is \boxed{} in². (type an exact answer in terms of π.)

Explanation:

Step1: Recall the formula for the area of a circle

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

Step2: Identify the radius from the diagram

From the diagram, the radius \( r \) of the circle is 10 inches.

Step3: Substitute the radius into the formula

Substitute \( r = 10 \) into the formula \( A = \pi r^2 \). We get \( A = \pi \times (10)^2 \).

Step4: Simplify the expression

Simplify \( (10)^2 \) to get 100. So the area \( A = 100\pi \).

Answer:

\( 100\pi \)