$\"\"$

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(a).

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The company sells cylindrical oil container with a capacity of $\"\"$ liters.

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$\"\"$ liter $\"\"$ c.c

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Therefore the volume of the container $\"\"$ is $\"\"$ c.c.

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The formula for the volume of the container is $\"\"$ .

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Now subustiute volume $\"\"$ $\"\"$ in the formula $\"\"$ .

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$\"\"$

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The formula for the surface area of the cylinder is $\"\"$ .

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Now subustiute $\"\"$ in the formula $\"\"$ .

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$\"\"$ .

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$\"\"$

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The surface area of the cylinder in terms or radius is given by $\"\"$ .

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$\"\"$

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(b).

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The company wants the surface area of the cylinder to be less than $\"\"$ sq.cms

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Subustiute $\"\"$ in the equation $\"\"$ .

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$\"\"$

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The inequality can be written as $\"\"$ .

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$\"\"$

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(c).

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The inequality is $\"\"$ .

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Let $\"\"$ .

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Draw the coordinate plane.

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Graph the function $\"\"$ .

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Graph :

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$\"\"$

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Observe the graph :

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The zeros of the graph are at $\"\"$ and $\"\"$ .

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The graph is undefined at $\"\"$ .

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The solutions of $\"\"$ are $\"\"$ values such that $\"\"$ is negative.

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From the graph the solution set is $\"\"$ .

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Since the radius is not in negative terms, only possible values are to be considered.

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Therefore the radius of the cylinder is between $\"\"$ cms to $\"\"$ cms.

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$\"\"$

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(a).

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The surface area of the function as a radius is given by $\"\"$ .

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(b).

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The inequality can be written as $\"\"$ .

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(c).

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Graph :

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$\"\"$

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Therefore the radius of the cylinder is between $\"\"$ cms to $\"\"$ cms.