Find the Volume of the Solid Obtained by Rotating the Region

question 72

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) \(2 \pi \left( e ^ { 10 } - e ^ { 2 } \right)\)

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Definitions:

Creek

A Native American people historically inhabiting the southeastern United States, renowned for their rich cultural heritage, including their art, rituals, and governance structures.

British Loyalists

Were colonists in America who remained loyal to the British throne during the American Revolutionary War.

Cherokee

The Cherokee are a Native American people historically settled in the southeastern United States, now primarily in Oklahoma and North Carolina, known for their rich culture, language, and forced relocation events like the Trail of Tears.

Gold

A chemical element with the symbol Au, gold is a precious metal known for its use in jewelry, currency, and various industrial applications due to its conductivity and resistance to corrosion.