# 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.