Find the Volume of the Indicated Region $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 81$

question 329

Multiple Choice

Find the volume of the indicated region.
-the region that lies inside the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 81$ and outside the cylinder $x ^ { 2 } + y ^ { 2 } = 25$

• A) \(\frac { 5 \left( 729 - 56 ^ { 3 / 2 } \right) \pi } { 2 }\)
• B) \(\frac { 3 \left( 729 - 56 ^ { 3 / 2 } \right) \pi } { 2 }\)
• C) \(\frac { 2 \left( 729 - 56 ^ { 3 / 2 } \right) \pi } { 3 }\)
• D) \(\frac { 4 \left( 729 - 56 ^ { 3 / 2 } \right) \pi } { 3 }\)

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Definitions:

Valence Electrons

The electrons in the outermost shell of an atom, which determine the atom's chemical properties and its ability to form bonds.

Hydrogen Bonds

Weak bonds between a hydrogen atom in one molecule and an electronegative atom (often oxygen or nitrogen) in another, important in the structure of water and DNA.

Carbon Atom

The fundamental chemical element with symbol C, essential to all known life forms and the basis of organic chemistry.

Carboxyl Group

A weakly acidic functional group; abbreviated —COOH.