Find the Area of the Surface $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16$

question 30

Multiple Choice

Find the area of the surface. The part of the sphere $x ^ { 2 } + y ^ { 2 } + z ^ { 2 } = 16$ that lies above the plane $z = 1$ .

• A) \(24 \pi\)
• B) \(\frac { \pi } { 16 }\)
• C) \(24\)
• D) \(\pi\)
• E) \(24 - \pi\)

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Definitions:

Surplus

The condition that occurs when the quantity of a good or service supplied exceeds the quantity demanded, often leading to a decrease in prices.

Shortage

An instance in the marketplace where the need for a product or service outstrips its provision.

Equilibrium Price

The cost at which the supply and demand for goods are equal.

Quantity Demanded

The total amount of a good or service that consumers are willing and able to purchase at a given price in a specified period.