Find the Volume of the Solid Generated by Revolving the Region

question 153

Multiple Choice

Find the volume of the solid generated by revolving the region about the y-axis.
-The region in the first quadrant bounded on the left by $y = x ^ { 3 }$ , on the right by the line $x = 2$ , and below by the $x$ -axis

• A) \(4 \pi\)
• B) \(\frac { 32 } { 5 } \pi\)
• C) \(\frac { 64 } { 5 } \pi\)
• D) \(\frac { 96 } { 5 } \pi\)

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Definitions:

Evaluate

The process of determining the value of an algebraic expression by substituting numbers into the variables and performing the operations.

Function

A link between a group of inputs and a set of possible outputs, ensuring that every input matches precisely one output.

Function

A relationship or expression involving one or more variables, where each input value has exactly one output value.

Simplify

To reduce a mathematical expression or equation to its simplest form by performing operations and combining like terms.