To find the radius of a circle when you know the area, you can use the formula for the area of a circle:
[tex]\[ A = \pi \cdot r^2 \][/tex]
where [tex]\( A \)[/tex] is the area and [tex]\( r \)[/tex] is the radius.
Given the area [tex]\( A = 144 \)[/tex] square inches, we can set up the equation:
[tex]\[ 144 = \pi \cdot r^2 \][/tex]
To solve for [tex]\( r \)[/tex], we need to isolate [tex]\( r \)[/tex]. Start by dividing both sides of the equation by [tex]\( \pi \)[/tex]:
[tex]\[ \frac{144}{\pi} = r^2 \][/tex]
Next, take the square root of both sides to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \sqrt{\frac{144}{\pi}} \][/tex]
When we solve this square root, we find that:
[tex]\[ r = 6.770275002573076 \][/tex]
Thus, the radius [tex]\( r \)[/tex] of the circle is approximately:
[tex]\[ r \approx 6.770275002573076 \][/tex]
Since the question asks for a simplified answer in integer or fraction form, we should leave the answer at this precise value because it cannot be simplified further in exact integer form without approximation.
