a spherical balloon is being in being inflated at a rate of 3cm^3/s. how fast is the radius increasing when the radius of the balloon is 4cm?

Question

It is about related rates, in the shape of a balloon

Answer 1

a spherical balloon is being in being inflated at a rate of 3cm^3/s. how fast is the radius increasing when the radius of the balloon is 4cm?

 

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Let V be the volume

      t - time

      E - the radius

 

We got V(t) and R(t) changing in time with

 

dV/dt=const=3cm^3/s

 

dV/dt=4/3pi*3R^2dR/dt = 4piR^2dR/dt=3(cm^3/s)

 

We need to find thr R(t) ( dependence in order to find dR/dt at R=4cm).

 

So,

 

DR/dt = 3/(4piR^2)

 

Evaluate this for R=4cm