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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? |
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Answer» 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.` |
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