Find the Volume of the Described Solid $x$ -Axis At $x = - 5$

question 11

Multiple Choice

Find the volume of the described solid.
-The solid lies between planes perpendicular to the $x$ -axis at $x = - 5$ and $x = 5$ . The cross sections perpendicular to the $x$ -axis are circular disks whose diameters run from the parabola $y = x ^ { 2 }$ to the parabola $y = 50 - x ^ { 2 }$ .

• A) \(\frac { 500 } { 3 } \pi\)
• B) \(\frac { 10000 } { 3 } \pi\)
• C) \(\frac { 5000 } { 3 } \pi\)
• D) \(5000 \pi\)

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Definitions:

Basicity

A measure of a substance's ability to donate electrons or accept protons, commonly applied in the context of acids and bases.

Nucleophilic

Characteristic of a chemical species that donates an electron pair to an electrophile to form a chemical bond in reaction.

t-Butoxide

A strong, non-nucleophilic base, often used in organic synthesis, derived from tertiary butanol.

Ethoxide

An alkoxide derived from ethanol, used as a strong base in organic synthesis, with the formula CH3CH2O-.