Find the Area of the Surface Generated by Revolving the Curve

question 104

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:

Connections

The relationships or links between people, places, devices, or concepts that allow for communication, interaction, or transfer of information.

Nature

The phenomena of the physical world collectively, including plants, animals, the landscape, and other features and products of the earth, as opposed to humans or human creations.

Submarine

A watercraft capable of independent operation underwater, often used for naval or research purposes.

Hydrosphere

All the waters on the earth's surface, such as lakes and seas, and sometimes including water over the earth's surface, such as clouds.