Define the relationship

The surface area of a sphere is given by $S = 4\pi r^2$. Since $4\pi$ is a constant, the area is directly proportional to the square of the radius, $S \propto r^2$.

$S = 4\pi r^2$

Apply successive percentage formula

When a quantity changes by $x\%$ twice (due to the square), the total percentage change is given by the formula $x + x + \frac{x^2}{100}$.

$20 + 20 + \frac{20 \times 20}{100}$

Calculate the result

Substituting $x = 20$ into the formula, we get $40 + \frac{400}{100} = 40 + 4 = 44\%$.

$44\%$