A Balloon in the Shape of a Sphere Is Deflating $V ( r ) = \frac { 4 } { 3 } \pi r ^ { 3 }$

question 83

Multiple Choice

A balloon in the shape of a sphere is deflating. Given that t represents the time, in minutes, since it began losing air, the radius of the balloon (in cm) is r(t) =23- t . Let the equation $V ( r ) = \frac { 4 } { 3 } \pi r ^ { 3 }$ represent the volume of a sphere of radius r . Find and interpret $( \mathrm { V } \circ \mathrm { r } ) ( \mathrm { t } )$

• A) \(( \mathrm { V } \circ \circ \mathrm { r } ) ( \mathrm { t } ) = 23 - \frac { 4 } { 3 } \pi ( 23 - \mathrm { t } ) ^ { 3 }\) ; This is the volume of the air lost by the balloon (in cm³) as a function of time (in minutes).
• B) \(( \mathrm { V } \circ \mathrm { r } ) ( \mathrm { t } ) = \frac { 4 } { 3 } \pi ( 23 - \mathrm { t } ) ^ { 3 }\) ; This is the volume of the air lost by the balloon (in cm³) as a function of time (in minutes).
• C) \(( V \circ r ) ( t ) = \frac { 4 } { 3 } \pi ( 23 - t ) ^ { 3 }\) ; This is the volume of the balloon (in cm³ ) as a function of time (in minutes).
• D) \(( \mathrm { V } \circ \mathrm { r } ) ( \mathrm { t } ) = \frac { 4 } { 3 } \pi ( \mathrm { t } - 23 ) ^ { 3 }\) ; This is the volume of the balloon (in cm³ ) as a function of time (in minutes).

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Definitions:

Total Surplus

The sum of consumer and producer surplus, representing the total net benefit to society from the production and consumption of goods or services.

AC

Short for Alternating Current, a type of electrical current where the flow of electric charge periodically reverses direction.

MC

Marginal Cost, the increase in total cost that arises from producing one additional unit of a product or service.

Natural Monopoly

A type of monopoly that arises due to high fixed or start-up costs associated with a business which makes it impractical for more than one firm to produce the same product or service efficiently.