Find the Volume of the Indicated Region $\mathrm { z } = 64 - \mathrm { x } ^ { 2 } - \mathrm { y }$

question 223

Multiple Choice

Find the volume of the indicated region.
-the region in the first octant bounded by the coordinate planes and the surface $\mathrm { z } = 64 - \mathrm { x } ^ { 2 } - \mathrm { y }$

• A) \(\frac { 131,072 } { 15 }\)
• B) 8192
• C) \(\frac { 32,768 } { 3 }\)
• D) \(\frac { 65,536 } { 9 }\)

---

Definitions:

Capital Fund

A fund created for the purpose of undertaking capital projects or investing in long-term assets, funded by capital expenditures or external financing sources.

General Fund

The primary operating fund of a government, covering general operations and services not accounted for in special-purpose funds.

Direct Increase

A rise in the value or quantity of something without intervening steps or intermediaries.

Endowment Fund

A fund where the principal amount is kept intact while the investment income is available for use, typically for the ongoing support of an organization.