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

question 85

Multiple Choice

Find the area of the surface generated by revolving the curve about the given axis. $x = 3 \cos ^ { 3 } \theta , y = 3 \sin ^ { 3 } \theta , 0 \leq \theta \leq \pi / 2$
(i) $x$ -axis;(ii) $y$ -axis

• A)(i) \(\frac { 27 } { 5 } \pi\); (ii) \(\frac { 27 } { 5 } \pi\)
• B)(i) \(\frac { 54 } { 5 } \pi\); (ii) \(\frac { 54 } { 5 } \pi\)
• C) (i) \(\frac { 27 } { 10 } \pi\); (ii) \(\frac { 27 } { 5 } \pi\)
• D) (i) \(\frac { 54 } { 5 } \pi\); (ii) \(\frac { 27 } { 5 } \pi\)
• E) (i) \(\frac { 54 } { 5 } \pi\); (ii) \(\frac { 108 } { 5 } \pi\)

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Definitions:

Psychoanalysis

A therapeutic technique and theory of psychological disorders, emphasizing unconscious conflicts and childhood experiences.

Cognitive Therapies

Psychological treatments that focus on changing faulty or irrational thinking patterns, beliefs, and attitudes.

Systematic Desensitization

A therapeutic method used to cure phobias and other behavior problems involving anxiety, by gradual exposure to the feared object or situation in a controlled environment.

Token Economy

An operant conditioning procedure in which people earn a token for exhibiting a desired behavior and can later exchange the tokens for privileges or treats.