Find the Exact Area of the Surface Obtained by Rotating $$x = 2 \cos ^ { 3 } \theta , \quad y = 2 \sin ^ { 3 } \theta , \quad 0 \leq \theta \leq \pi / 2$$

question 23

Multiple Choice

Find the exact area of the surface obtained by rotating the given curve about the x-axis. $$x = 2 \cos ^ { 3 } \theta , \quad y = 2 \sin ^ { 3 } \theta , \quad 0 \leq \theta \leq \pi / 2$$

• A) \(\frac { 24 \pi } { 5 }\)
• B) \(\frac { 18 \pi } { 5 }\)
• C) \(\frac { 12 \pi } { 5 }\)
• D) \(\frac { 2 \pi } { 4 }\)
• E) None of these

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Definitions:

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A body plan in which there are two symmetrical halves of the body, with a distinct left and right, matching one another.