The surface area of a sphere is 7.84pift^2. What is the radius of this sphere?

1 answer

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:

\[ \boxed{1.4} , \text{ft} \]