The formula for the surface area \( A \) of a sphere is given by:
\[ A = 4\pi r^2 \]
where \( r \) is the radius of the sphere.
Given that the surface area is \( 7.84\pi , \text{ft}^2 \), we can set up the equation:
\[ 4\pi r^2 = 7.84\pi \]
To simplify, we can divide both sides by \( \pi \) (assuming \( \pi \neq 0 \)):
\[ 4r^2 = 7.84 \]
Next, divide both sides by 4:
\[ r^2 = \frac{7.84}{4} = 1.96 \]
Now, take the square root of both sides to find \( r \):
\[ r = \sqrt{1.96} \]
Calculating the square root:
\[ r = 1.4 , \text{ft} \]
Thus, the radius of the sphere is:
\[ \boxed{1.4} , \text{ft} \]