The total surface area A of a cylinder with a fixed volume of 1000cm³ is given by the formula A=2πx²+2000/x where x cm is the radius. Show that when the rate of change of the area with respect to the radius is zero, x³=500/π

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

the answer is a.

step-by-step explanation:

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step-by-step explanation: