Find the Volume of the Solid Generated by Revolving the Region

question 12

Multiple Choice

Find the volume of the solid generated by revolving the region about the given line.
-The region in the first quadrant bounded above by the line $y = 1$ , below by the curve $y = \sqrt { \sin 3 x }$ , and on the left by the $y$ -axis, about the line $y = - 1$

• A) \(\frac { 1 } { 2 } \pi ^ { 2 } - \frac { 1 } { 9 } \pi\)
• B) \(\frac { 1 } { 6 } \pi ^ { 2 } - \frac { 1 } { 3 } \pi\)
• C) \(\frac { 1 } { 2 } \pi - \frac { 1 } { 9 }\)
• D) \(\frac { 1 } { 6 } \pi ^ { 2 } + \frac { 1 } { 3 } \pi\)

---

Definitions:

Chain-Weighted System

An inflation measure that adjusts the weights from year to year in calculating a price index, thereby reducing the bias caused by a fixed-price weighting system.

Nominal Gross Domestic Product (GDP)

The market value of all goods and services produced within a country in a given period, measured without adjusting for inflation.

Real GDP

The total value of all goods and services produced by a country in a year, adjusted for inflation, making it a measure of economic output that accounts for changes in the price level.

GDP Price Index

An indicator reflecting the variation in costs for all newly produced domestic final goods and services within an economy.