Calculate the Area of the Surface S $S$ Is the Portion of the Paraboloid

question 250

Multiple Choice

Calculate the area of the surface S.
- $S$ is the portion of the paraboloid $z = 3 x ^ { 2 } + 3 y ^ { 2 }$ that lies between $z = 4$ and $z = 5$ .

• A) \(\frac { \pi } { 9 } [ 101 \sqrt { 101 } - 65 \sqrt { 65 } ]\)
• B) \(\frac { 1 } { 27 } [ 101 \sqrt { 101 } - 65 \sqrt { 65 } ]\)
• C) \(\frac { \pi } { 54 } [ 101 \sqrt { 101 } - 65 \sqrt { 65 } ]\)
• D) \(\frac { \pi } { 27 } [ 101 \sqrt { 101 } - 65 \sqrt { 65 } ]\)

---

Definitions:

Objects

Instances of classes that encapsulate data and functionality, acting as the basic building blocks of object-oriented programming.

Class ActionListener

An interface in Java that listens for action events, such as button presses, allowing classes to react to user interactions.

ActionEvent

An object that represents an action event in Java, such as pressing a button or entering text in a text field.

Method

A block of code designed to perform a specific task, associated with an object or class in programming.