The Volume of a Can That Is 12 Centimeters (Cm) $( r ) = 37.68 r ^ { 2 }$

question 8

Essay

The volume of a can that is 12 centimeters (cm) tall is approximated by the function v $( r ) = 37.68 r ^ { 2 }$ , where r is the radius of the can in cm. Chicken soup costs $0.01 per milliliter (mL) and since $1 \mathrm {~mL} = 1 \mathrm {~cm} ^ { 3 }$ , we can say that chicken soup costs $0.01 \text { per } \mathrm { cm } ^ { 3 }$ . The cost to fill a 12 cm tall can with chicken soup is given by C(v) = 0.01v, where v is the volume of the can in $\mathrm { cm } ^ { 3 }$ .
a. Find $( C \circ v ) ( r )$ and interpret its meaning in the context of this problem.
b. Approximate to the nearest cent the cost to fill a 12 cm can with chicken soup if the can's radius is 5 cm.

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Definitions:

Behavioral Economics

A field of study blending economics and psychology to explore how people make decisions, often deviating from rationality.

Constrained Maximization

The process of finding the maximum value of a function subject to certain constraints, often used in economics and optimization problems.

Psychological Factors

Elements that influence a consumer's purchasing behavior and decision-making process, including motivations, perceptions, attitudes, and beliefs.

Economic Transaction

An event or agreement in which goods, services, or assets are exchanged between parties for money or its equivalent.