Find the Volume of the Indicated Region $z = x ^ { 2 } + y ^ { 2 }$

question 100

Multiple Choice

Find the volume of the indicated region.
-the region that lies under the paraboloid $z = x ^ { 2 } + y ^ { 2 }$ and above the triangle enclosed by the lines $x = 8 , y = 0$ , and $y = 2 x$

• A) \(\frac { 1792 } { 3 }\)
• B) 8192
• C) \(\frac { 14,336 } { 3 }\)
• D) \(\frac { 224 } { 3 }\)

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Definitions:

Contribution Margin

The sum by which the income from sales surpasses variable expenses, showing the extent to which revenue aids in covering fixed costs and generating profit.

High-low Method

A technique used in accounting and finance to estimate variable and fixed costs based on the highest and lowest levels of activity.

Variable Component

An element of cost or expense that varies directly with changes in production volume, business activity, or other drivers.

Contribution Margin Ratio

The percentage of each sales dollar remaining after variable costs have been deducted, indicating how much contributes to fixed costs and net profit.