# Worksheet: Surface of Revolution of Parametric Curves

In this worksheet, we will practice using integration to find the area of the surface of revolution of a parametrically defined 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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**Q3: **

Determine the surface area of the solid obtained by rotating the parametric curve and , where , about the .

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**Q4: **

Determine the surface area of the solid obtained by rotating the parametric curve and , where , about the .

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**Q5: **

Determine the surface area of the solid obtained by rotating the parametric curve and , where about the . Approximate your answer to the nearest decimal place.

**Q6: **

Calculate the surface area of the solid obtained by revolving the curve given by the parametric equations and such that about the line . Round your answer to two decimal places.

**Q7: **

Calculate the surface area of the solid obtained by revolving the curve given by the parametric equations and such that about the . Round your answer to two decimal places.

**Q8: **

Calculate the surface area of the solid obtained by revolving the curve given by the parametric equations and such that about the . Round your answer to two decimal places.

**Q9: **

Calculate the surface area of the solid obtained by revolving the curve given by the parametric equations and such that about the . Round your answer to two decimal places.

**Q10: **

Calculate the surface area of the solid obtained by revolving the curve given by the parametric equations and such that about the line . Round your answer to two decimal places.