Question

find the area of the given geometric figure. if the figure is a circle, give an exact area and then use 3.14 as an approximation for π to approximate the area. d = 17 in. the exact area of the circle is (simplify your answer. type an exact answer in terms of π.) the approximate area of the circle is (simplify your answer. type a whole number or decimal rounded to the nearest thousandth as needed.)

Explanation:

Step1: Find the radius

The diameter \( d = 17 \) in, so the radius \( r=\frac{d}{2}=\frac{17}{2}=8.5 \) in.

Step2: Calculate the exact area

The formula for the area of a circle is \( A = \pi r^2 \). Substituting \( r = 8.5 \), we get \( A=\pi\times(8.5)^2=\pi\times72.25 = 72.25\pi \) square inches.

Step3: Calculate the approximate area

Using \( \pi\approx3.14 \), the area \( A\approx3.14\times72.25 = 226.865 \) square inches.

Answer:

The exact area of the circle is \( 72.25\pi \) square inches.
The approximate area of the circle is \( 226.865 \) square inches.