Question

Find how fast (a) the volume, (b) the surface area, (c) the diagonal, of
a cube increases when the length of the edge increases

Answer 1

A) Let $V_0$ – initial the volume and $V_1$ - the volume when the length of the edge increases, $a_0$ – initial length of the edge, $a_1$ – new length of the edge, then $V_1=\frac{a_1^3}{a_0^3}\times V_0$ .

B) Let $S_0$ - initial the surface area and $S_1$ - the surface area when the length of the edge increases, $a_0$ – initial length of the edge, $a_1$ – new length of the edge, then $S_1=\frac{a_1^2}{a_0^2}\times S_0$ .

C) Similar to the previous example $d_1=\frac{a_1^2}{a_0^2}\times d_0$ .