Find the Volume of the Solid Obtained by Rotating the Region

question 59

Multiple Choice

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. $y=\ln x, y=1, y=3, x=0 \text {; about the } y \text { - axis }$

• A) \(\frac{\pi}{2}\left(e^{3}+1\right)\)
• B) \(\frac{\pi}{2}\left(e^{6}-e^{2}\right)\)
• C) \(\frac{e^{6}}{2}\)
• D) \(\frac{e^{6}-e^{3}}{2}\)
• E) None

---

Definitions:

Consumption

Families engaging in the use of products and services.

Income

Sums of money attained, usually on a fixed schedule, from work or investment undertakings.

Interest Rate

The proportion at which principal loaned money is repaid with interest to the lender over time, usually as an annual rate.

Utility Function

A mathematical representation that ranks individuals' or entities' preferences over a set of goods or outcomes.