The formula for the surface area \( S \) of a sphere is given by:
\[ S = 4\pi r^2 \]
where \( r \) is the radius of the sphere. Given that the surface area \( S \) is 7.84 square feet, we can set up the equation:
\[ 4\pi r^2 = 7.84 \]
To find \( r^2 \), we can rearrange the equation:
\[ r^2 = \frac{7.84}{4\pi} \]
Now, let's calculate \( r^2 \):
- Calculate \( 4\pi \):
\[ 4\pi \approx 4 \times 3.14 \approx 12.56 \]
- Divide 7.84 by \( 4\pi \):
\[ r^2 = \frac{7.84}{12.56} \approx 0.6241 \]
- Now, take the square root to find \( r \):
\[ r = \sqrt{0.6241} \approx 0.79 \text{ feet} \]
Thus, the radius of the sphere is approximately \( 0.79 \) feet.