To find the radius of a circle given its area, we will use the formula for the area of a circle: [tex]\( A = \pi r^2 \)[/tex], where [tex]\( A \)[/tex] is the area and [tex]\( r \)[/tex] is the radius.
Given:
Area [tex]\( A = 125 \)[/tex] square inches
We need to solve for the radius [tex]\( r \)[/tex]. Follow these steps:
1. Start with the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
2. Plug the given area into the formula:
[tex]\[ 125 = \pi r^2 \][/tex]
3. Isolate [tex]\( r^2 \)[/tex] by dividing both sides of the equation by [tex]\( \pi \)[/tex]:
[tex]\[ r^2 = \frac{125}{\pi} \][/tex]
4. Take the square root of both sides to solve for [tex]\( r \)[/tex]:
[tex]\[ r = \sqrt{\frac{125}{\pi}} \][/tex]
At this point, we find that the radius [tex]\( r \)[/tex] is approximately [tex]\( 6.3078313050504 \)[/tex] inches.
5. Finally, round the calculated radius to the nearest tenth:
[tex]\[ r \approx 6.3 \][/tex]
So, the radius of the circle, rounded to the nearest tenth, is [tex]\( 6.3 \)[/tex] inches.
