A can in the shape of a right circular cylinder is required to have a volume of 500 cubic centimeters. The top and bottom are made of a material that costs 11 cents per square centimeter, while the sides are made of a material that costs 8 cents per square centimeter. Express the total cost C of the material as a function of the radius r of the cylinder.

The answer to the question is

The total cost C of the material as a function of the radius r of the cylinder is

0.6912·r² + 800/r Dollars.

Step-by-step explanation:

To solve the question, we note that

The area of the top and bottom combined = 2·π·r²

The area of the sides = 2·π·r·h

and the volume = πr²h = 500 cm²

Therefore height = 500 / (πr²)

Substituting the value of h into the area of the side we have

Area of the side = 2πr·500 / (πr²) = 1000/r

Therefore total area of can = Area of top + Area of bottom + Area of side

Whereby the cost of the can = 0.11*Area of top + 0.11*Area of bottom + 0.8*Area of side

Which is equal to

0.11*2*π*r² + 0.8*1000/r = 0.6912·r² + 800/r

The cost of the can is $ (0.6912·r² + 800/r)