In this worksheet, we will practice finding the area of the surface of revolution for a parametrized curve.

**Q1: **

Consider the parametric equations and , where .The area of the surface obtained by rotating this parametric curve radians about the -axis can be calculated by evaluating the integral where .

Find .

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Hence, find the surface area of by evaluating the integral.

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**Q2: **

Consider the parametric equations and , where . Calculate the area of the surface obtained when the curve is rotated radians about the -axis.

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