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).

---

Definitions:

Fair Value

An estimate of the market value of an asset or liability, reflecting current conditions and market perceptions.

Voting Stock

Shares in a company that grant the holder the right to vote on corporate matters, typically related to the election of the board of directors.

Contingent Payment

A payment that is due only if specific conditions are met, typically used in agreements where future outcomes can influence the amount or timing of the payment.

Cash Flows

The total amount of money being transferred into and out of a business, especially as affecting liquidity.