Answer:
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)
