The radius of the earth is approximately 3,960 miles. find the approximate surface-area-to-volume ratio of the earth.

The surface area of a sphere is          A = 4π R²

The volume of a sphere is                  V = (4/3) ( π) (R³)

The ratio of  (surface area) to (volume) is

                                                  4 π R² / (4/3) (π) (R³)

Divide top and bottom by 4π :      R² / (1/3)     (R³)

Multiply top and bottom by 3:      3 R² / R³

Divide top and bottom by  R² :       3 / R .

For the Earth,

             A / V  =  (3) / (3,960 miles)  =  0.00076 per mile (rounded)