You are asked for "the dimensions of the can", which will betwovalues: the radius and the height. You seem to have arrived at only one value...?

Since 1 mL = 1cc, the volume (in terms of linear units) is 500 cc. Since the costs are given in terms of square meters, though, we'll have to convert. Since 100 cm = 1 m, then 10 000 cm^2 = 1 m^2 and 1 000 000 cc = 1 m^3. Then 500 cc = 0.0005 m^3.

The relevant equations are:

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. . . . .

. . . . .

We can solve the "volume" equation for h in terms of r:

. . . . .

Then the "cost" function is:

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Differentiating with respect to "r" gives:

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Setting equal to "zero" gives:

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. . . . .

I don't get your answerorthe book's, but I've probably gone wrong somewhere...