Use Cylindrical Coordinates to Evaluate the Triple Integral $$\iiint _ { E } y d V$$

question 47

Multiple Choice

Use cylindrical coordinates to evaluate the triple integral $$\iiint _ { E } y d V$$
where $E$ is the solid that lies between the cylinders $x ^ { 2 } + y ^ { 2 } = 3$ and $x ^ { 2 } + y ^ { 2 } = 7$ above the $x y$ -plane and below the plane $z = x + 4$ .

• A) \(8.57\)
• B) 0
• C) \(3.4\)
• D) \(9.19\)
• E) \(0.54\)

---

Definitions:

Variable Cost

Costs that vary directly with the level of production or services provided, such as materials and labor.

Net Income

The total profit or loss of a company after all expenses, taxes, and costs have been subtracted from total revenue.

Fixed Cost

A cost that does not change with an increase or decrease in the number of goods or services produced or sold.

Production Costs

Direct costs associated with the manufacturing of goods, including labor, materials, and overhead expenses.