Find the Area of the Inner Loop Of $r = 3 + 6 \sin \theta$

question 7

Multiple Choice

Find the area of the inner loop of $r = 3 + 6 \sin \theta$

• A)
• \(27 \pi + \frac { 27 \sqrt { 2 } } { 2 }\)
• B)
• \(9 \pi - \frac { 27 \sqrt { 3 } } { 4 }\)
• C)
• \(27 \pi - \frac { 27 \sqrt { 3 } } { 4 }\)
• D)
• \(9 \pi - \frac { 27 \sqrt { 3 } } { 2 }\)
• E)
• \(9 \pi + \frac { 27 \sqrt { 2 } } { 2 }\)

---

Definitions:

Jellylike Matrix

A viscous, gelatinous substance that provides structural support and medium for cell components in various tissues, including the extracellular matrix of connective tissue.

Schistosomiasis

A disease caused by infection with freshwater parasitic worms in certain tropical and subtropical regions.

Typhus

A group of infectious diseases caused by Rickettsia bacteria, transmitted by lice, fleas, or mites, characterized by severe fever, headache, and rash.

Malaria

A serious disease caused by Plasmodium parasites, transmitted to humans through the bite of infected Anopheles mosquitoes, characterized by fever, chills, and flu-like illness.