Solve the Problem B) C) D)

question 62

Multiple Choice

Solve the problem.
-Let D be the smaller cap cut from a solid ball of radius 6 units by a plane 2 units from the center of the sphere. Set up the triple integral for the volume of D in rectangular coordinates.

• A) \(\int _ { - \sqrt { 32 } } ^ { \sqrt { 32 } } \int _ { - \sqrt { 32 - x ^ { 2 } } } ^ { \sqrt { 32 - x ^ { 2 } } } \int _ { 2 } ^ { \sqrt { 36 - x ^ { 2 } - y ^ { 2 } } } d z d y d x\)
• B) \(\int _ { - \sqrt { 32 } } ^ { \sqrt { 32 } } \int _ { - \sqrt { 32 - x ^ { 2 } } } ^ { \sqrt { 32 - x ^ { 2 } } } \int _ { 6 } ^ { \sqrt { 4 - x ^ { 2 } - y ^ { 2 } } } d z d y d x\)
• C) \(\int _ { - \sqrt { 40 } } ^ { \sqrt { 40 } } \int _ { - \sqrt { 32 - x ^ { 2 } } } ^ { \sqrt { 32 - x ^ { 2 } } } \int _ { 2 } ^ { \sqrt { 36 - x ^ { 2 } - y ^ { 2 } } } d z d y d x\)
• D) \(\int _ { - \sqrt { 40 } } ^ { \sqrt { 40 } } \int _ { - \sqrt { 32 - x ^ { 2 } } } ^ { \sqrt { 32 - x ^ { 2 } } } \int _ { 6 } ^ { \sqrt { 4 - x ^ { 2 } - y ^ { 2 } } } d z d y d x\)

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Definitions:

Micro Pole

A segment or aspect of social analysis that focuses on small-scale interactions and individual experiences.

Individual Thought

The process of thinking or reasoning conducted by an individual, emphasizing personal beliefs, ideas, and cognitive processes.

Macro-Micro Continuum

A concept in sociology that explains the range of social interactions from large-scale institutions and systems (macro) to individual personal interactions (micro).

Global Structure

Global structure signifies the overarching system or patterns that govern international relations, global economies, or worldwide social networks, highlighting interconnectivity on a global scale.