$\"\"$

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Given that surface area (T) of a cone = 359 square feet.

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Slant height(l) of a cone = 15 ft.

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Surface area(T):

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$\"\"$ (Surface area of a cone)

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Divide each side by $\"\"$ )

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$\"\"$ (Simplify) $\"\"$ $\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Multiply: $\"\"$ )

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$\"\"$ (Divide: $\"\"$ )

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$\"\"$ (Multiply each side by 15)

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$\"\"$ (Simplify)

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$\"\"$ (Subtract 114 from each side)

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$\"\"$ (Simplify)

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$\"\"$

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$\"\"$

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$\"\"$ (Substitute $\"\"$ )

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$\"\"$ (Simplify)

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$\"\"$ (Add: $\"\"$ )

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$\"\"$ (Use a calculator)

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$\"\"$

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$\"\"$ (Simplify)

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$\"\"$ (Divide)

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Neglect negative value because radius is always positive.

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$\"\"$

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$\"\"$

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The radius is approximately 5.5 feets.