$$\text { Set up the iterated integral for evaluating } \iint _ { D } \int f ( r , \theta , z ) d z r d r d \theta \text { over the given region D. }$$

question 217

Multiple Choice

$$\text { Set up the iterated integral for evaluating } \iint _ { D } \int f ( r , \theta , z ) d z r d r d \theta \text { over the given region D. }$$
- $\mathrm { D }$ is the solid right cylinder whose base is the region between the circles $r = 7 \cos \theta$ and $r = 8 \cos \theta$ , and whose top lies in the plane $z = 9 - y$ .

• A) \(\int _ { 0 } ^ { 2 \pi } \int _ { 7 \cos \theta } ^ { 8 \cos \theta } \int _ { 0 } ^ { 9 - r \sin \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta\)
• B) \(\int _ { 0 } ^ { \pi } \int _ { 7 \cos \theta } ^ { 8 \cos \theta } \int _ { 0 } ^ { 9 - \sin \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } r \mathrm { dr } d \theta\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 7 } ^ { 8 \cos \theta } \int _ { 0 } ^ { 9 - \sin \theta } \mathrm { cos } \theta ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta\)
• D) \(\int _ { 0 } ^ { \pi } \int _ { 7 } ^ { 8 \cos \theta } \int _ { 0 } ^ { 9 - r \sin \theta } \mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) \mathrm { dz } \mathrm { rdr } \mathrm { d } \theta\)

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Definitions:

Direct Materials Quantity Variance

A measure used to evaluate the efficiency of the quantity of materials used in production, calculated as the difference between the standard cost of direct materials and the actual cost of direct materials used.

Actual Costs

The real expenditure incurred in the manufacturing or production of goods and services, as opposed to estimated costs.

Standard Costs

Predetermined or estimated costs of manufacturing, selling, or performing a service, used as benchmarks against actual costs for budgetary control and performance measurement.

Price Variances

Differences between the actual prices paid for goods or services and the expected or standard prices.