(a)

Volume of the cubic crustal is , Where is its side length.

Here side length is measured in mm.

.

Differentiate on each side with respect to .

Substitute in above expression.

.

.

This is the rate of change of volume with respect to is mm³/mm.

(b)

The surface area of the cube is , Where is its side length.

Consider .

Substitute in above expression.

.

Hence rate of change of volume with respect to its side length is half of surface area.

Volume of cube with increased side length of is .

If is small, then can approximate .

Rate of change of area of new sphere with respect to radius can be considered as

(a) .

(b) Rate of change of volume with respect to its side length is half of surface area.