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

question 144

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 $\mathrm { x }$ -axis are circular disks whose diameters run from the parabola $y = x ^ { 2 }$ to the parabola $y = 32 - x ^ { 2 }$ .

• A) \(\frac { 256 } { 3 } \pi\)
• B) \(\frac { 8192 } { 5 } \pi\)
• C) \(\frac { 16384 } { 15 } \pi\)
• D) \(\frac { 8192 } { 15 } \pi\)

Apply the method of difference to identify causal relationships.

Analyze the role of disconfirming evidence in strengthening generalizations.

Understand how the method of concomitant variations contributes to identifying causal relations.

Apply the method of residues to infer additional causal factors in complex scenarios.