Find the Surface Area Generated by Rotating the Lemniscate $r ^ { 2 } = 10 \cos 2 \theta$

question 15

Multiple Choice

Find the surface area generated by rotating the lemniscate $r ^ { 2 } = 10 \cos 2 \theta$ about the line $\theta = \pi$ .

• A) \(2 \pi \sqrt { 10 }\)
• B) \(2 \pi \sqrt { 10 } ( 2 - \sqrt { 2 } )\)
• C) \(\pi \sqrt { 10 }\)
• D) \(\frac { \pi \sqrt { 10 } } { 10 }\)
• E) \(\frac { \pi } { 10 }\)

---

Definitions:

Inductive Reasoning

A method of reasoning in which specific observations lead to broader generalizations or theories.

Deductive Reasoning

A logical process where a conclusion follows necessarily from the given premises; if the premises are true, the conclusion must also be true.

Problem Solving

The mental process of finding an appropriate way to attain a goal when the goal is not readily available.

Heritability

The proportion of variation among individuals in a population that can be attributed to genetic variations.