The volume of a cube is increasing at a rate of 7 `cm^(2)//sec.` How fast is the suface area increasing when the length of an edge is 4cm?

Explanation

Let at some time t, the length of edge is x cm.
`v= x^(3) " "rArr " "(dv)/(dt)= 3x^(2) (dx)/(dt) "("but .(dv)/(dt) =7")"`
`rArr " "(dx)/(dt)= (7)/(3x^(2)) cm//sec`
`"Now" " "S=6x^(2)`
`(dS)/(dt)= 12x .(dx)/(dt) " "rArr " "(dS)/(dt)=12x.(7)/(3x^(2)) =(28)/(x)`
`" when "" "x=4 cm. (dS)/(dt)=7 cm^(2)//sec.`