Find the Volume of the Described Solid $x$ -Axis At $x = \pi / 6$

question 91

Multiple Choice

Find the volume of the described solid.
-The solid lies between planes perpendicular to the $x$ -axis at $x = \pi / 6$ to $x = \pi / 2$ . The cross sections perpendicular to the $x$ -axis are circular disks with diameters running from the curve $y = \cot x$ to the curve $y = \csc x$ .

• A) \(\frac { ( \sqrt { 3 } - 1 ) \pi } { 2 } - \frac { \pi ^ { 2 } } { 12 }\)
• B) \(( \sqrt { 3 } - 1 ) \pi + \frac { \pi ^ { 2 } } { 6 }\)
• C) \(( 2 \sqrt { 3 } - 2 ) \pi - \frac { \pi ^ { 2 } } { 3 }\)
• D) \(\frac { ( \sqrt { 3 } + 1 ) \pi } { 2 } - \frac { \pi ^ { 2 } } { 6 }\)

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