Solve the Problem $\delta ( x , y , z ) = \frac { 1 } { 81 - x ^ { 2 } - y ^ { 2 } }$

question 424

Multiple Choice

Solve the problem.
-Find the mass of the region of density $\delta ( x , y , z ) = \frac { 1 } { 81 - x ^ { 2 } - y ^ { 2 } }$ bounded by the paraboloid $z = 81 - x ^ { 2 } - y ^ { 2 }$ and the $x y$ -plane.

• A) \(6561 \pi\)
• B) \(729 \pi\)
• C) \(9 \pi\)
• D) \(81 \pi\)

---

Definitions:

Craft Unions

Unions composed of workers specialized in a particular craft or trade, focusing on specific job skills and worker rights within that profession.

Monopsony Power

A market condition where there is only one buyer for a product or service, giving that buyer considerable control over prices.

Professional Athletes

Individuals who compete in sporting activities at the highest level and receive payment for their performance and participation.

Professional Sports

Sporting activities or events where athletes receive payment for their performance, as opposed to amateur sports where athletes do not receive financial compensation.