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 \( A = 7.84\pi \) ft², we can set up the equation:
\[ 4\pi r^2 = 7.84\pi \]
We can divide both sides of the equation by \( \pi \):
\[ 4r^2 = 7.84 \]
Now, divide both sides by 4:
\[ r^2 = \frac{7.84}{4} \]
Calculating the right side:
\[ r^2 = 1.96 \]
Now take the square root of both sides to find the radius:
\[ r = \sqrt{1.96} \]
Calculating the square root:
\[ r = 1.4 \text{ ft} \]
So, the radius of the sphere is \( 1.4 \) ft.
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