Solve the Problem $\mathrm { D }$ Be the Region Bounded Below by the Cone

question 106

Multiple Choice

Solve the problem.
-Let $\mathrm { D }$ be the region bounded below by the cone $z = \sqrt { x ^ { 2 } + y ^ { 2 } }$ and above by the sphere $z = \sqrt { 4 - x ^ { 2 } - y ^ { 2 } }$ . 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) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 2 / \sqrt { 2 } } \int _ { 0 } ^ { z } r d r d z d \theta + \int _ { 0 } ^ { 2 \pi } \int _ { 2 / \sqrt { 2 } } ^ { 2 } \int _ { 0 } ^ { \sqrt { 8 - z ^ { 2 } } } r d r d z d \theta\)
• B) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 2 / 2 } \int _ { 0 } ^ { z } r d r d z d \theta + \int _ { 0 } ^ { 2 \pi } \int _ { 2 / 2 } ^ { 2 } \int _ { 0 } ^ { \sqrt { 8 - z ^ { 2 } } } r d r d z d \theta\)
• C) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 2 / 2 } \int _ { 0 } ^ { \mathrm { z } } \mathrm { rdrdz } \mathrm { d } \theta + \int _ { 0 } ^ { 2 \pi } \int _ { 2 / 2 } ^ { 2 } \int _ { 0 } ^ { \sqrt { 4 - \mathrm { z } ^ { 2 } } } \mathrm { rdr } \mathrm { dz } \mathrm { d } \theta\)
• D) \(\int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 2 / \sqrt { 2 } } \int _ { 0 } ^ { z } r d r d z d \theta + \int _ { 0 } ^ { 2 \pi } \int _ { 2 / \sqrt { 2 } } ^ { 2 } \int _ { 0 } ^ { \sqrt { 4 - z ^ { 2 } } } r d r d z d \theta\)

Realize the significance of knowledge sharing and social constructivism in learning environments.

Comprehend the impact of technological advancements and web-based instruction on training methodologies.

Appreciate the role of learning professionals in fostering performance improvement and managing learning programs.

Recognize the influence of external factors like demographics and social media on Learning 2.0.

---

Definitions:

Elasticity

Elasticity refers to the economic concept describing the change in the behavior of buyers and sellers in response to a change in price or other factors.

Flexibility

is the quality of being able to adapt to new, different, or changing requirements, in both personal and professional contexts.

Grid Computing

A distributed architecture of large numbers of computers connected to solve a complex problem.

Scalability

The ability of a system, network, or process to handle a growing amount of work, or its potential to be enlarged to accommodate that growth.