Question

an open box with a square base have a volume of 8m^3. the material of the base costs $8 per square meter and the material for the sides costs $6 per square meter. express the cost of the materials as a function of the width (w) of the base

Answer 1

(Refer to picture for diagram.)

Area of base $=w^{2}$
Area of one side $=\frac{8}{w^{2}}*w=\frac{8}{w}$

Cost of base material $=8w^{2}$
Cost of material for a side $=6*\frac{8}{w}=\frac{48}{w}$
There are 4 sides so $4*\frac{48}{w}=\frac{192}{w}$

Total cost $C(w)=8w^{2}+\frac{192}{w}$