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).