As a spherical cell doubles its radius, how do its surface area and volume change?

1. Surface area of a sphere scales as the square of the radius. 2. Volume of a sphere scales as the cube of the radius. 3. Doubling the radius multiplies the square term by two squared, which is four. 4. Doubling the radius multiplies the cube term by two cubed, which is eight. 5. Surface area therefore rises fourfold while volume rises eightfold. 6. The two cannot rise by the same factor, because a square and a cube of the same number differ once the number exceeds one. 7. Area up fourfold and volume up eightfold is the correct pairing. _Source: OpenStax Biology (1st ed., CC BY 4.0), Ch 4 "Cell Structure", section 4.2 Prokaryotic Cells_