$\"\"$

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(a)

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The curve is $\"\"$ and the interval is $\"\"$ .

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(i)

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The surface area formula, for rotation about the $\"\"$ - axis is $\"\"$ .

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Consider $\"\"$ .

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Solve for $\"\"$ .

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$\"\"$

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Evaluate boundaries :

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If $\"\"$ , then $\"\"$ .

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If $\"\"$ , then $\"\"$ .

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$\"\"$

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Consider $\"\"$ .

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Differentiate the above equation with respect to $\"\"$ .

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$\"\"$

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Substitute corresponding values in $\"\"$ .

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The surface area :

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$\"\"$

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The surface area of the curve obtained after rotation about $\"\"$ - axis is $\"\"$ .

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$\"\"$

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(ii)

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The surface area formula, for rotation about the $\"\"$ - axis is $\"\"$ .

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Substitute corresponding values in $\"\"$ .

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The surface area :

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$\"\"$

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The surface area of the curve obtained after rotation about $\"\"$ - axis is $\"\"$ .

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$\"\"$

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(b)

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From part (a) :

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(i)

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The surface area of the curve obtained after rotation about $\"\"$ - axis is $\"\"$ .

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Using a calculator, the value of $\"\"$ is $\"\"$ .

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From part (a) :

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(ii)

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The surface area of the curve obtained after rotation about $\"\"$ - axis is $\"\"$ .

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Using a calculator, the value of $\"\"$ is $\"\"$ . $\"\"$

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(a)

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(i) $\"\"$ .

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(ii) $\"\"$ .

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(b)

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(i) $\"\"$ .

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(ii) $\"\"$ .