Question 1163173
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            After reading the posts of the two other respectful tutors,  I have a feeling

            that another solution should be written and presented in more clear form.



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The volume of a sphere is  V = {{{(4/3)*pi*r^3}}}.


Since both the volume and the radius depend on time, the formula becomes  V(t) = {{{(4/3)*pi*r^3(t)}}}.


The derivative over time is  {{{(dV)/(dt)}}} = {{{4*pi*r^2(t)*((dr)/(dt))}}}


Hence,  {{{(dr)/(dt)}}} = {{{((dV)/(dt))/(4*pi*r^2(t))}}} = {{{120/(4*pi*15^2)}}}.   (1)


The surface area of a sphere is  A = {{{4*pi*r^2}}},  or  A(t) = {{{4*pi*r^2(t)}}}.


The derivative over time is  {{{((dA)/(dt))}}} = {{{4*pi*2*r(t)*((dr)/(dt))}}} = {{{8*pi*r(t)*((dr)/(dt))}}}


Substitute here  the expression  {{{(dr)/(dt)}}} = {{{120/(4*pi*15^2)}}}  from (1)  and r(t) = 15 cm.  You will get


    {{{((dA)/(dt))}}} = {{{8*pi*15*(120/(4*pi*15^2))}}} = {{{(8*15*120)/(4*15^2)}}} = {{{(2*120)/15}}} = 2*8 = 16 cm^2/min.
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Solved.