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:

Production Possibilities Curve

A graphical representation that shows the maximum quantity of one good that can be produced for every possible level of production of another good, assuming a fixed amount of resources.

Opportunity Costs

The cost of forgoing the next best alternative when making a decision or choosing between options.

Production Possibilities Frontier (PPF)

A curve depicting the maximum output possibilities for two goods, given a set of inputs and technology, illustrating the trade-offs in production choices.

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