To find the area of a circle with a given radius, we use the formula for the area of a circle:
[tex]\[ A = \pi r^2 \][/tex]
where
- [tex]\( A \)[/tex] is the area,
- [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.14159,
- [tex]\( r \)[/tex] is the radius of the circle.
Given that the radius ([tex]\( r \)[/tex]) is 15 inches, we substitute this value into the formula:
[tex]\[ A = \pi (15)^2 \][/tex]
First, we calculate the square of the radius:
[tex]\[ 15^2 = 225 \][/tex]
Next, we multiply this result by [tex]\( \pi \)[/tex]:
[tex]\[ A = \pi \times 225 \][/tex]
By performing this multiplication, we find:
[tex]\[ A \approx 706.9 \][/tex]
So, the area of the circle, rounded to the nearest tenth of a square inch, is 706.9 square inches.
Among the given options:
- 225.0 in²
- 47.1 in²
- 94.2 in²
- 706.5 in²
The closest value to our calculated result of 706.9 in² is not exactly listed, but since the correct answer must be rounded to the nearest tenth, the nearest value given is 706.5 in². Given additional calculations confirming the accuracy, but based on the options provided, 706.9 in² should be the most accurate answer.
