The surface area \( A \) of a sphere is given by the formula:
\[ A = 4\pi r^2 \]
where \( r \) is the radius of the sphere.
In your case, the surface area is given as \( 7.84\pi \) ft². We can set up the equation:
\[ 4\pi r^2 = 7.84\pi \]
To simplify, we can divide both sides of the equation by \( \pi \):
\[ 4r^2 = 7.84 \]
Next, divide both sides by 4:
\[ r^2 = \frac{7.84}{4} = 1.96 \]
Now take the square root of both sides to find the radius \( r \):
\[ r = \sqrt{1.96} = 1.4 \]
Thus, the radius of the sphere is:
\[ \boxed{1.4} \text{ ft} \]