Find the Area of the Surface $S$ Where $S$ Is the Part of the Sphere

question 12

Short Answer

Find the area of the surface $S$ where $S$ is the part of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16$ that lies inside the cylinder $x ^ { 2 } - 4 x + y ^ { 2 } = 0$ .

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Definitions:

Sigmoid Colon

The part of the large intestine that is closest to the rectum and anus.

Transverse Colon

The middle part of the large intestine, passing across the abdomen from right to left below the stomach.

Descending Colon

The part of the large intestine that descends from the splenic flexure to the sigmoid colon, involved in water and electrolyte absorption.

Hypopharynx

The lower part of the pharynx (throat) that lies just above the esophagus and larynx, important in the process of swallowing.