Asked Oct 16, 2019

A spherical snowball melts at a rate proportional to its surface area. Show that the rate of change of the radius is constant. (hint: surface area: 4(pi)r^2)


Expert Answer

Step 1

Given that spherical snow ball melts at a rate proportional to its surface area

Show that rate of change of radius is constant


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let volume of snow ball is V 4 know that volume of sphere is given by V=r 3 dV according to question rate of change of volume dt dV dV -=kx4 dt where k constant, area (A ) =4ur2

Step 2

It is kwon that volume is a function of r...


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dV dV dr dt dr dt dV 4 dr so, dr kx4m2 - 4m dt dr k dt


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