解答
If the ratio of corresponding linear dimensions is $k = \frac{L_1}{L_2}$, the ratio of surface areas is $k^2 = \frac{A_1}{A_2}$ and the ratio of volumes is $k^3 = \frac{V_1}{V_2}$.
解説
If a solid has its linear dimensions tripled ($k = 3$), its surface area increases by $3^2 = 9$ times, and its volume increases by $3^3 = 27$ times.