Air is being pumped into a spherical balloon at a constant rate such that its radius increases constantly with respect to time according to the equation r(t)=0.5t^2+r_0, (where r is in cm,t is in minute and r_0 is the initial radius of the balloon). Then the rate of change of its volume after 2 minute is...

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Christine Sosa · Accepted Answer

V  (  r  )  =      4    3        π        r    3                d      V              d      t        =      4    3        π    ×  3      r    2              d      r              d      t        =  4      π        r    2              d      r              d      t        .  .  .  .  .  .  (  1  )    r  (  t  )  =  0.5      t    2    +      r    ∘      ⇒  r  (  2  )  =  0.5  ×  4  +  2  =  4  c  m                      d        r                    d        t                    t      =      2        =  t  +  0  =  2  c  m      /    m  i  n              d      V              d      t        =  128      π    c      m    3        /    m  i  n

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