Find the Exact Area of the Surface Obtained by Rotating $x = 2 \cos ^ { 3 } \theta , \quad y = 2 \sin ^ { 3 } \theta , \quad 0 \leq \theta \leq \pi / 2$

question 13

Multiple Choice

Find the exact area of the surface obtained by rotating the given curve about the x-axis. $x = 2 \cos ^ { 3 } \theta , \quad y = 2 \sin ^ { 3 } \theta , \quad 0 \leq \theta \leq \pi / 2$

• A) \(\frac { 24 \pi } { 5 }\)
• B) \(\frac { 18 \pi } { 5 }\)
• C) \(\frac { 12 \pi } { 5 }\)
• D) \(\frac { 2 \pi } { 4 }\)
• E) None of these

---

Definitions:

Total Liabilities

Represents the combined debts and obligations that a company owes to outside parties at a specific point in time.

Asset

Any resource owned or controlled by a business or an individual that is expected to produce future economic value.

Stockholders' Equity

The residual interest in the assets of a corporation after deducting its liabilities, representing ownership equity spread among stockholders.

Liabilities

Financial obligations or debts owed by a company to external parties or individuals.