To find the maximum radius of the basketball plushy that can be created from 171.9 square inches of fabric, we start with the formula for the surface area of a sphere, which is given by:
\[ A = 4\pi r^2 \]
Where:
- \( A \) is the surface area,
- \( r \) is the radius,
- \( \pi \) is approximately 3.14.
We want to solve for \( r \) by setting \( A = 171.9 \) square inches:
\[ 171.9 = 4 \cdot 3.14 \cdot r^2 \]
First, we calculate \( 4 \cdot 3.14 \):
\[ 4 \cdot 3.14 = 12.56 \]
Now we can substitute this back into the equation:
\[ 171.9 = 12.56 \cdot r^2 \]
Next, we divide both sides by 12.56 to isolate \( r^2 \):
\[ r^2 = \frac{171.9}{12.56} \]
Calculating the right side:
\[ r^2 \approx \frac{171.9}{12.56} \approx 13.68 \]
Now we take the square root of both sides to find \( r \):
\[ r \approx \sqrt{13.68} \approx 3.7 \]
Therefore, the maximum radius of the basketball plushy that can be created is approximately \( 3.7 \) inches.
Thus, the correct answer is:
3.7 in