Find the Volume of the Solid Generated by Revolving the Region

question 1

Multiple Choice

Find the volume of the solid generated by revolving the region bounded by the graphs of the equations about the given lines. $x = y ^ { 2 } , x = 8 y - y ^ { 2 }$
(i) $y$ -axis; (ii) the line $x = 18$

• A) \(\frac { 1,024 } { 3 } \pi ; \frac { 1,280 } { 3 } \pi\)
• B) \(\frac { 16 } { 3 } \pi ; \frac { 128 } { 3 } \pi\)
• C) \(\frac { 64 } { 3 } \pi ; \frac { 128 } { 3 } \pi\)
• D) \(\frac { 64 } { 3 } \pi ; \frac { 1,280 } { 3 } \pi\)
• E) \(\frac { 16 } { 3 } \pi ; \frac { 1,280 } { 3 } \pi\)

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Definitions:

Proximity to Market

The closeness of a business or production site to its buyers or consumers, which can reduce transportation costs and improve supply chain efficiency.