Use the Method of Cylindrical Shells to Find the Volume $y = x ^ { 2 } , y = 0 , x = 1 , x = 6 ;$

question 4

Multiple Choice

Use the method of cylindrical shells to find the volume of solid obtained by rotating the region bounded by the given curves about the specified axis. $y = x ^ { 2 } , y = 0 , x = 1 , x = 6 ;$ about $x = 1$

• A) \(18,150 \pi\)
• B) \(3,025 \pi\)
• C) \(\frac { 6 \pi } { 3,025 }\)
• D) \(3,413 \pi\)
• E) \(\frac { 3,025 \pi } { 6 }\)

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Definitions:

Tension

A force that stretches a material, attempting to elongate it.

Shear

A strain resulting from forces causing parts of a material to slide past each other in opposite directions.

Confining

Pertaining to geological layers or conditions that restrict the flow of groundwater due to lower permeability.

Foliation

The planar arrangement of textural or structural features in metamorphic rocks and certain igneous rocks.