Find the Volume of the Described Solid $x$ -Axis At $x = - 4$

question 234

Multiple Choice

Find the volume of the described solid.
-The solid lies between planes perpendicular to the $x$ -axis at $x = - 4$ and $x = 4$ . The cross sections perpendicular to the $x$ -axis between these planes are squares whose bases run from the semicircle $y = - \sqrt { 16 - x ^ { 2 } }$ to the semicircle $y = \sqrt { 16 - x ^ { 2 } }$ .

• A) \(\frac { 128 } { 3 }\)
• B) \(\frac { 256 } { 3 }\)
• C) \(\frac { 512 } { 3 }\)
• D) \(\frac { 1024 } { 3 }\)

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Definitions:

Economies Of Scale

The cost advantages that enterprises obtain due to their scale of operation, with cost per unit of output generally decreasing with increasing scale.

Diseconomies

Negative effects on costs that occur as a business expands, typically resulting from inefficiencies that stem from managerial and operational challenges.

Expansion Path

A curve in input space showing how the optimal mix of inputs changes as the firm expands output.

Fixed Proportion

Refers to a production process where inputs must be used in strict, unchanging ratios to produce an output.