Find the Volume of the Solid Obtained by Rotating the Region

question 7

Multiple Choice

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line.
$y = \ln x , y = 1 , y = 5 , x = 0$ ; about the $y$ - axis

• A) \(\frac { \pi } { 4 } \left( e ^ { 10 } - e \right)\)
• B) \(\frac { \pi } { 2 } \left( 1 - e ^ { 10 } \right)\)
• C) \(\frac { \pi } { 2 } \left( e ^ { 10 } - e ^ { 2 } \right)\)
• D) \(\frac { \pi e ^ { 10 } } { 2 }\)
• E) \(2 \pi \left( e ^ { 10 } - e ^ { 2 } \right)\)

---

Definitions:

Organizational Behavior

The study of how people interact within groups and organizations and how this behavior affects the performance of the organizations.

Computer Science

The study of algorithmic processes, computational machines, and computation itself.

Natural Sciences

Academic disciplines that study the natural world, using empirical evidence and scientific methods.

Knowledge Acquisition

The process by which individuals or systems gather information and understanding about a subject, leading to learning and the development of expertise.