Question

what is the radius of a sphere with a surface area of 7.84pie ft^2

Answer 1

To find the radius of a sphere from its surface area, we can use the formula for the surface area of a sphere:

\[
A = 4\pi r^2
\]

where \( A \) is the surface area and \( r \) is the radius. Given that the surface area \( A \) is \( 7.84\pi \) ft², we can set up the equation:

\[
4\pi r^2 = 7.84\pi
\]

We can divide both sides by \( \pi \) (assuming \( \pi \neq 0 \)):

\[
4r^2 = 7.84
\]

Next, divide by 4:

\[
r^2 = \frac{7.84}{4}
\]
\[
r^2 = 1.96
\]

Now, take the square root of both sides to find \( r \):

\[
r = \sqrt{1.96}
\]

Calculating the square root gives:

\[
r = 1.4 \text{ ft}
\]

So, the radius of the sphere is \( 1.4 \) ft.