Use the Shell Method to Find the Volume of the Solid

question 127

Multiple Choice

Use the shell method to find the volume of the solid generated by revolving the shaded region about the indicated line.
-About the line $y = - 6$


$$\begin{array} { l } x = y + 6 \\x = y ^ { 2 }\end{array}$$

• A) \(192 \pi\)
• B) \(\frac { 387 } { 4 } \pi\)
• C) \(\frac { 63 } { 2 } \pi\)
• D) \(\frac { 387 } { 2 } \pi\)

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Definitions:

Object Permanence

The understanding that objects continue to exist even when they cannot be observed (seen, heard, touched, smelled, or sensed in any way).

Conservation of Volume

A cognitive ability in child development where the understanding that volume remains unchanged even when its shape changes is recognized.

Egocentrism

The inability to differentiate between oneself and other people, often characterized by a lack of empathy and an overemphasis on one's own perspective.

Cross-modal Transference

The ability to transfer sensory information from one modality to another, such as identifying objects by touch that have only been seen before.