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:

Labor

The effort by individuals to produce goods or services in exchange for wages or salary.

Wages

Payments made by employers to employees for their labor, typically calculated on an hourly, daily, or piecework basis.

Marginal Revenue Product

The additional revenue produced by adding one more unit of a specific input (like labor), assuming other inputs remain constant.

Perfect Competitor

A hypothetical market scenario where numerous small firms compete against each other, and none of them can influence the market price.