Question 1142721
.


What is written in the post - is INCORRECT.



<pre>
The volume of a sphere   V(r) = {{{(4/3)*pi*r^3}}},  <U>as EVERYBODY knows</U>.


From the formula,  {{{(dV)/(dt)}}} = {{{(dV)/(dr)}}}.{{{((dr)/(dt))}}} = {{{(4/3)*3*pi*r^2}}}.{{{((dr)/(dt))}}} = {{{4*pi*r^2}}}.{{{((dr)/(dt))}}}.


Substitute here  {{{(dV)/(dt)}}} = 2 cm^3/s,  which is given.  You will get


                 2 = {{{4*pi*r^2}}}.{{{((dr)/(dt))}}},


hence,


                {{{((dr)/(dt))}}} = {{{(1/2)*(1/(pi*r^2))}}},


totally different from what is written in your post.
</pre>


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To get the answer to your question, simply substitute  r= 54  into my last formula.