Proportions and Dimensions

$\displaystyle S.A. = 4πr^2$

$\displaystyle V = \frac 43πr^3$

If the radius of a sphere increases by $\displaystyle \Delta r$ , then its surface area will increase in squared proportions - in other words, by $\displaystyle (\Delta r)^2$ . Similarly, its volume increases in cubic proportions, by $(\Delta r)^3$ .

$\Delta S.A. = (\Delta r)^2$

$1.44 = (\Delta r)^2$

$\Delta r = 1.2$

$1.2^3 = 1.728$

Thus, the volume increases by $72.8 \%$ .