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.

Solution:

The volume of the can = 500 cubic centimeters

We know that

The volume of a right circular cylinder = πr²h

500 = πr²h

So height h = 500/πr²

The formula to find the area of the sides = 2πrh

Substituting the value of h

= 2πr (500/πr²)

= 1000/r

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

Cost of can = 0.11×Area of top +0.11×Area of bottom + 0.8×Area of side

So we get

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

Therefore, cost of can is $(0.6912·r² + 800/r).

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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.

Summary:

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. The total cost C of the material as a function of the radius r of the cylinder is $(0.6912·r² + 800/r).