$\"\"$

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Volume of the steel drum $\"\"$ .

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Formula for the volume of cylinder is $\"\"$ , where $\"\"$ is radius and $\"\"$ is height.

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$\"\"$

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$\"\"$ .

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(a)

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Find the function $\"\"$ .

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The steel drum has a top and bottom.

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Surface area of the cylinder is $\"\"$ .

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$\"\"$ .

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Substitute $\"\"$ .

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$\"\"$

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$\"\"$

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(b)

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Find the amount of material, if the drum radius is $\"\"$ :

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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The area is approximately $\"\"$ .

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$\"\"$

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(c)

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Find the amount of material, if the drum radius is $\"\"$ :

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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The area is approximately $\"\"$ .

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$\"\"$

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(d)

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Find the amount of material, if the drum radius is $\"\"$ :

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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The area is approximately $\"\"$ .

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$\"\"$

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(e)

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Graph the function $\"\"$ :

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Identify the minimum point.

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Graph of the function $\"\"$ :

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$\"\"$

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Observe the graph:

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The minimum point occurs at $\"\"$ .

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Therefore, the area is smallest when $\"\"$ .

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(a) $\"\"$ .

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(b) $\"\"$ .

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(c) $\"\"$ .

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(d) $\"\"$ .

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(e) $\"\"$ .