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.