Find the Area of the Surface $\mathbf { r } ( u , v ) = u \cos v \mathbf { i } + u \sin v \mathbf { j } + u ^ { 2 } \mathbf { k }$

question 49

Multiple Choice

Find the area of the surface. The part of the paraboloid $\mathbf { r } ( u , v ) = u \cos v \mathbf { i } + u \sin v \mathbf { j } + u ^ { 2 } \mathbf { k }$ ; $0 \leq u \leq 7$ , $0 \leq v \leq 2 \pi$

• A) \(\frac { \pi ( 197 \sqrt { 197 } - 1 ) } { 12 }\)
• B) \(\frac { \pi ( 197 \sqrt { 197 } - 1 ) } { 3 }\)
• C) \(\frac { \pi ( 197 \sqrt { 197 } - 1 ) } { 6 }\)
• D) \(\frac { 5 \pi ( 197 \sqrt { 197 } - 1 ) } { 12 }\)

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Definitions:

Output Module

A component in a control system that sends signals or power from the system to the external environment.

PLC System

A PLC system (Programmable Logic Controller) is a digital computer used for automation of electromechanical processes, such as control of machinery on factory assembly lines.

Programming Terminal

A combination of keyboard and monitor used to insert, modify, and observe programs stored in a PLC.

Preventive Maintenance

Scheduled maintenance activities designed to prevent equipment failures before they occur.