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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.
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).
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).
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