Find the Area of the Part of the Sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 25 z$

question 93

Multiple Choice

Find the area of the part of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 25 z$ that lies inside the paraboloid $z = x ^ { 2 } + y ^ { 2 }$ .

• A) \(11.5 \pi\)
• B) \(9.5 \pi\)
• C) \(25 \pi\)
• D) \(5 \pi\)
• E) \(15 \pi\)

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Definitions:

Common Iliac Artery

A large artery that divides into the internal and external iliac arteries, supplying blood to the pelvis and lower limbs.

Bifurcation

Bifurcation refers to the process or point at which a structure divides into two branches or parts, often used in reference to blood vessels or branching patterns in biology.

Abdominal Aorta

The largest artery in the abdominal cavity that delivers oxygen-rich blood to the abdominal organs, pelvis, and legs.

Thoracic Wall

The bony and muscular structures forming the chest cavity that protect thoracic organs and assist in breathing.