SOLUTION: Hi, I need help
A cube is expanding in such a way that its sides are changing at a rate of
2 cm s^( - 1). Find the rate of change of the total surface area when its volume is
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-> SOLUTION: Hi, I need help
A cube is expanding in such a way that its sides are changing at a rate of
2 cm s^( - 1). Find the rate of change of the total surface area when its volume is
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Question 1170709: Hi, I need help
A cube is expanding in such a way that its sides are changing at a rate of
2 cm s^( - 1). Find the rate of change of the total surface area when its volume is 125 cm^3. Answer by ikleyn(52786) (Show Source):
The surface area of a cube is S(a) = 4a^2, where "a" is the edge size.
We have edge size depending on time a = a(t); therefore, the rate of the surface area change is the derivative
S'(t) = 4*2*a(t)*a'(t) = 8*a(t)*a'(t) . (1)
The value a'(t) is given : it is a'(t) = 2 cm/s.
The value of "a" is a= 5, when the volume is 125 cm^3.
Therefore, the rate of the surface area change is, according the formula (1),
S'(t) = 8*5*2 = 80 . ANSWER
