Answer:
Totalcost = [tex]\frac{24}{r}[/tex]+ [tex]\frac{2r^2}{3}[/tex]
Step-by-step explanation:
Given the volume of the can is 24 cubic cm
Also given that it costs 3 cents per square cm on the to and bottom sides And 2 cents per square cm on the curved sides
Let the radius and height of the can be r and h
Now Volume = π[tex]hr^{2}[/tex]
24 = π[tex]hr^{2}[/tex]
πh = [tex]\frac{24}{r^{2} }[/tex]
Now for constructing we use the surface area which is
Total surface area = lateral surface area + curved surface area
Lateral suface area = 2π[tex]r^2[/tex]
Cost for preparing the lateral surface is lateral surface / cost for top and bottom = [tex]\frac{2r^2}{3}[/tex]
Curved surface area = 2πrh = 2r [tex]\times \frac{24}{r^2}[/tex] = [tex]\frac{48}{r}[/tex]
Cost for preparing theCurved surface area is Curved surface / cost for curved sides = [tex]\frac{48}{r\times 2}= \frac{24}{r}[/tex]
Totalcost = [tex]\frac{24}{r}[/tex]+ [tex]\frac{2r^2}{3}[/tex]
