Find the Volume of the Solid Generated by Revolving the Region

question 30

Multiple Choice

Find the volume of the solid generated by revolving the region about the given line.
-The region bounded above by the line $y = 8$ , below by the curve $y = 8 \cos ( \pi x )$ , on the left by the line $x = - 0.5$ , and on the right by the line $x = 0.5$ , about the line $y = 8$

• A) \(32 \pi\)
• B) \(192 \pi - 128\)
• C) \(96 \pi\)
• D) \(96 \pi - 256\)

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Definitions:

Gene Tree

Gene tree refers to the branched genealogical lineage of homologous alleles that traces their evolution back to an ancestral allele.

Species Tree

A representation of the evolutionary relationships among various species based on genetic data.

Coalescence Time

The time in the past where two or more gene sequences found in a sample population have a common ancestor.

Branch Lengths

In phylogenetics, measurements that represent the evolutionary distance or time between points in a phylogenetic tree.