To find the radius of the spherical soap given the surface area, we can use the formula for the surface area of a sphere:
\[ A = 4\pi r^2 \]
where \( A \) is the surface area and \( r \) is the radius. In this case, we know that the surface area \( A \) is \( 63.585 \) square inches.
We can rearrange the formula to solve for the radius \( r \):
\[ r^2 = \frac{A}{4\pi} \]
Now, substituting the given surface area into the formula, we have:
\[ r^2 = \frac{63.585}{4\pi} \]
Calculating \( 4\pi \):
\[ 4\pi \approx 4 \times 3.14159 \approx 12.56636 \]
Now we can continue with the calculation:
\[ r^2 \approx \frac{63.585}{12.56636} \approx 5.06 \]
To find \( r \), we take the square root of \( r^2 \):
\[ r \approx \sqrt{5.06} \approx 2.25 \text{ inches} \]
So, the radius of the spherical soap is approximately \( 2.25 \) inches.
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