To find the approximate area of a circle with a given diameter, we follow these steps:
1. Determine the radius:
The radius of a circle is half of its diameter. Given that the diameter is 14 inches:
[tex]\[
\text{Radius} = \frac{\text{Diameter}}{2} = \frac{14 \, \text{inches}}{2} = 7 \, \text{inches}
\][/tex]
2. Use the formula for the area of a circle:
The formula for calculating the area [tex]\( A \)[/tex] of a circle is:
[tex]\[
A = \pi r^2
\][/tex]
where [tex]\( r \)[/tex] is the radius of the circle.
3. Substitute the radius into the formula:
Now we substitute the radius (7 inches) into the formula:
[tex]\[
A = \pi \times (7 \, \text{inches})^2
\][/tex]
4. Simplify the expression:
Calculate the square of the radius:
[tex]\[
(7 \, \text{inches})^2 = 49 \, \text{square inches}
\][/tex]
Then multiply by [tex]\( \pi \)[/tex]:
[tex]\[
A = \pi \times 49 \, \text{square inches} \approx 153.94 \, \text{square inches}
\][/tex]
Given that [tex]\( \pi \approx 3.14159 \)[/tex], the area of the circle is approximately:
[tex]\[
A \approx 153.94 \, \text{in}^2
\][/tex]
So the approximate area of the circle is:
D. [tex]\( 154 \, \text{in}^2 \)[/tex]
