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Algebra
Pregunta

7) A balloon in the shape of a sphere is deflating...

7) 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 \( r ( t ) = 20 - t \) Let the equation \( V ( r ) = \frac { 4 } { 3 } \pi r ^ { 3 } \) represent the volume of a sphere of radius \( r \) . Find and interpret \( ( V \circ r ) ( t ) \) .

A) \( ( V \circ r ) ( t ) = 20 - \frac { 4 } { 3 } \pi ( 20 - t ) ^ { 3 } \) ; this is the volume of the air lost by the balloon (in cm \( { } ^ { 3 } \) ) as a function of time (in minutes). 

B) \( ( V \circ r ) ( t ) = \frac { 4 } { 3 } \pi ( t - 20 j ^ { 3 } \) ; this is the volume of the balloon (in cm) as a function of time (in minutes).

C) \( ( V \circ r ) ( t ) = \frac { 4 } { 3 } \pi ( 20 - t ) ^ { 3 } \) ; this is the volume of the air lost by the balloon (in cm) as a function of time (in minutes). 

D) \( ( V \circ r ) ( t ) = \frac { 4 } { 3 } \pi ( 20 - t ) ^ { 3 } \) ; this is the volume of the balloon (in cm³) as a function of time (in minutes).  

Answer

 

Solución
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