Solve the Problem $D$ Be the Region Bounded Below by The $x y$

question 341

Multiple Choice

Solve the problem.
-Let $D$ be the region bounded below by the $x y$ -plane, above by the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 100$ , and on the sides by the cylinder $x ^ { 2 } + y ^ { 2 } = 81$ . Set up the triple integral in cylindrical coordinates that gives the volume of $D$ using the order of integration $\mathrm { dr } \mathrm { dz } \mathrm { d } \theta$ .

• A) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 19 } } \int _ { 0 } ^ { 10 } \mathrm { rdrdzd \theta } + \int _ { 0 } ^ { 2 \pi } \int _ { \sqrt { 19 } } ^ { 9 } \int _ { 0 } ^ { \sqrt { 81 - z ^ { 2 } } } \mathrm { rdrdzd \theta }\)
• B) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 19 } } \int _ { 0 } ^ { 9 } \mathrm { rdrdzd \theta } + \int _ { 0 } ^ { 2 \pi } \int _ { \sqrt { 19 } } ^ { 10 } \int _ { 0 } ^ { \sqrt { 100 - \mathrm { z } ^ { 2 } } } \mathrm { rdr } \mathrm { dz } d \theta\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 19 } } \int _ { 0 } ^ { 9 } r d r d z d \theta + \int _ { 0 } ^ { 2 \pi } \int _ { \sqrt { 19 } } ^ { 10 } \int _ { 0 } ^ { \sqrt { 81 - z ^ { 2 } } } r d r d z d \theta\)
• D) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { \sqrt { 19 } } \int _ { 0 } ^ { 10 } r d r d z d \theta + \int _ { 0 } ^ { 2 \pi } \int _ { \sqrt { 19 } } ^ { 9 } \int _ { 0 } ^ { \sqrt { 100 - z ^ { 2 } } } r d r d z d \theta\)

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Definitions:

Risk-free Rate

The hypothetical yield of a risk-free investment, commonly signified by the interest rate on government bonds.

Cumulative Return

Cumulative return is the aggregate amount of money gained or lost by an investment over a set period, typically expressed as a percentage.

Initial Margin

The portion of the purchase price that an investor must deposit when buying securities on margin; serves as a down payment on the investment.

Maintenance Margin

The minimum amount of equity that must be maintained in a margin account after a purchase has been made, to keep the account open.