The volume of a cube is increasing at the rate of . How fast is the
surface area increasing when the length of its edge is 12 cm?
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Let x be the strength of side, v be the volume & s be the surface area of cube
,where x is a function of![\frac{dv}{dt}= 8\frac{cm^{3}}{s} \left [ given \right ]](https://learn.careers360.com/latex-image/?%5Cfrac%7Bdv%7D%7Bdt%7D%3D%208%5Cfrac%7Bcm%5E%7B3%7D%7D%7Bs%7D%20%5Cleft%20%5B%20given%20%5Cright%20%5D)
![\frac{ds}{dt}= 12x\frac{8}{3x^{2}}\left [ using(i) \right ]\Rightarrow \frac{32}{x}](https://learn.careers360.com/latex-image/?%5Cfrac%7Bds%7D%7Bdt%7D%3D%2012x%5Cfrac%7B8%7D%7B3x%5E%7B2%7D%7D%5Cleft%20%5B%20using%28i%29%20%5Cright%20%5D%5CRightarrow%20%5Cfrac%7B32%7D%7Bx%7D)
Then
line t
Now
Now,
Hence when
then,