$\"\"$

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Given that Surface area(T) of cylinder = $\"\"$ square meters.

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Height(h) of cylinder = 12 meters.

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Use the formula for surface area to write and solve an equation for the radius.

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Surface area(T):

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$\"\"$ (Surface area of cylinder)

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

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

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$\"\"$ (Simplify)

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$\"\"$ (Subtract 160 from each side)

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$\"\"$ (Simplify)

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$\"\"$ (20r can be written as $\"\"$ )

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$\"\"$ (Apply distributive property)

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$\"\"$ (Take out common factor)

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$\"\"$ (Apply zero product propetry) \ \

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$\"\"$

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Since the radius of a circle cannot have a negative value,

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$\"\"$ is eliminated. So, the radius of the base is 4 centimeters.

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$\"\"$

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$\"\"$ Diameter(d):

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$\"\"$

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

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

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The diameter of the base is 16 meters.