Question

Which is the formula for the surface area of a sphere with diameter d?

Answer 1

The surface area of a sphere with radius r is going to be,\[\large\rm A=4\pi\left(\color{orangered}{r}\right)^2\]Recall that diameter is `twice the length` of the radius.\[\large\rm d=2\color{orangered}{r}\]

Answer 2

Solving for r in this relationship shows us that the radius is half the length of the diameter,\[\large\rm \color{orangered}{\frac{d}{2}=r}\]This is what we'll replace r with in our surface area equation.

Answer 3

\[\large\rm A=4\pi\left(\color{orangered}{\frac{d}{2}}\right)^2\]And then you can do some simplification from there if you like, squaring each of the numerator and denominator.