Solve the Problem $\mathrm { V }$ Of a Right Circular Cylinder of Height 2 and Radius

question 4

Multiple Choice

Solve the problem.
-The volume $\mathrm { V }$ of a right circular cylinder of height 2 and radius $\mathrm { r }$ is $\mathrm { V } ( \mathrm { r } ) = 2 \pi \mathrm { r } ^ { 2 }$ . Find the instantaneous rate of change of volume with respect to radius $r$ when $r = 7$ .

• A) \(23 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }\)
• B) \(28 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }\)
• C) \(98 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }\)
• D) \(32 \pi \mathrm { ft } ^ { 3 } / \mathrm { ft }\)

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Definitions:

Market Price

The amount of money that a product is bought or sold for in the marketplace; determined by supply and demand.

Surplus

A situation where the quantity supplied of a good exceeds the quantity demanded, often leading to lower prices or stored inventory.

Shortage

Occurs when the quantity demanded of a good exceeds its supply at a given price, leading to an unmet demand in the market.

Quantity Supplied

The total amount of a product or service that producers are willing and able to sell at a given price over a specified period.