Question

if a sphere has surface area 16π square feet, what is its diameter?

Explanation:

Step1: Write the formula for the surface area of a sphere

The formula for the surface area of a sphere is \(S = 4\pi r^{2}\), where \(S\) is the surface area and \(r\) is the radius.

Step2: Substitute the given surface area into the formula

Given \(S=16\pi\), we substitute into \(S = 4\pi r^{2}\):
\(16\pi=4\pi r^{2}\)

Step3: Solve for \(r^{2}\)

Divide both sides of the equation \(16\pi = 4\pi r^{2}\) by \(4\pi\):
\(\frac{16\pi}{4\pi}=r^{2}\)
\(4 = r^{2}\)

Step4: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius is a non - negative quantity), \(r=\sqrt{4}=2\) feet.

Step5: Calculate the diameter \(d\)

The diameter \(d\) of a sphere is related to the radius by \(d = 2r\). Substituting \(r = 2\) into this formula, we get \(d=2\times2 = 4\) feet.

Answer:

\(4\) feet