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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Quizplus · Accepted Answer

The correct formula for the volume of a sphere given its radius $r$ is $\frac{4}{3}\pi r^3$. Since $r(t) = 23 - t$, substituting $r(t)$ into the volume formula gives $\frac{4}{3}\pi (23 - t)^3$, which represents the volume of the balloon as a function of time.

A Balloon in the Shape of a Sphere Is Deflating V(r)=43πr3V ( r ) = \frac { 4 } { 3 } \pi r ^ { 3 }V(r)=34​πr3

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