Find the Volume of the Solid Obtained When the Region $y = x ^ { 3 }$

question 52

Multiple Choice

Find the volume of the solid obtained when the region bounded by the curves $y = x ^ { 3 }$ , $x = 1$ , and the x-axis is rotated about the line x = - 1.

• A) \(\frac { 127 \pi } { 3 }\)
• B) \(\frac { 62 \pi } { 3 }\)
• C) \(\frac { \pi } { 2 }\)
• D) \(\frac { \pi } { 4 }\)
• E) \(\frac { 2 \pi } { 5 }\)
• F) \(\frac { \pi } { 5 }\)
• G) \(\frac { 9 \pi } { 10 }\)
• H) \(\frac { 31 \pi } { 3 }\)

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Definitions:

Industrialization

The development of industries in a country or region on a wide scale, often leading to significant social, economic, and cultural changes.

Agricultural Development

The process and practices involved in improving farming methods and the production of crops and livestock to increase food supply, efficiency, and sustainability.

Politicization

The process of making an issue political, thereby bringing it into the domain of public debate and decision-making.

Global Order

The structured arrangement of power, institutions, and relationships that governs international relations and determines the global norms and policies.