$\"\"$

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Radius of sphere is $\"\"$ cms.

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Volume of the cone is $\"\"$ c.c

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Length is represented by $\"\"$ .

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Formula for volume of the cone is $\"\"$ .

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The height of the cone is $\"\"$ $\"\"$ .

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Subustiute $\"\"$ and $\"\"$ $\"\"$ in the formula $\"\"$ .

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$\"\"$ .

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$\"\"$

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$\"\"$

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The triangle formed by $\"\"$ which is length, the radius of the cone $\"\"$ , and the radius of the sphere $\"\"$ cms is a right triangle.

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Therefore $\"\"$ .

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$\"\"$

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Subustiute $\"\"$ in the obtained form of $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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Let $\"\"$ .

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Perform the synthetic division by using trail and error method subustiute $\"\"$ .

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$\"\"$

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Since $\"\"$ conclude that $\"\"$ is a zero of $\"\"$ .

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Therefore $\"\"$ is a rational zero.

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The remaining quadratic factor is $\"\"$ . $\"\"$

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The remaining quadratic factor $\"\"$ yeilds no rational zeros.

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Now use the quadratic formula to find the zeros.

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$\"\"$ .

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The quadratic factor is in the form of $\"\"$ .

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Where $\"\"$ .

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Now subustiute the values in the quadratic formula.

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The quadratic formula is $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$ and $\"\"$ .

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Therefore the rational zeros are $\"\"$ and $\"\"$ .

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The rational zeros are $\"\"$ , $\"\"$ and $\"\"$ .

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Consider $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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$\"\"$

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Since the length of $\"\"$ must be positive $\"\"$ is not to be considered.

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$\"\"$ cms or about $\"\"$ cms.

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$\"\"$

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Therefore length $\"\"$ cms or about $\"\"$ cms.