Determine the diameter of a piece of copper wire in mm. Can someone please help

Question

Determine the diameter of a piece of copper wire in mm.

Can someone please help me with this step-by-step? I've already tried 3 different answers (mostly just changing the sig figs or last digits) and none of them have been right.--> 0.332 mm radius (0.664 diameter) and 0.334 radius (0.668 diameter) are wrong answers as well.

**PLEASE BE CAREFUL ROUNDING SIGNIFICANT FIGURES FOR EACH STEP OF THE PROBLEM!! THIS IS ESSENTAIL TO GETTING THE CORRECT ANSWER AND CORRECT NUMBER OF SIGNIFICANT DIGITS AT THE END!!

Explanation / Answer

we have

h = 46.76 cm

mass of copper wire = 1.461 g

density of copper wire = 8.933 g/cm^3

therefore

volume of the copper wire = mass / density

or

volume of the copper wire = 1.461 g / 8.933 g/cm^3 = 0.1636 cm^3

and

volume of copper wire = (pi) * r^2 * h

or

0.1636 cm^3 = 3.14 x r^2 x 46.76 cm

or

r^2 = 0.001114

or

r = 0.03338 cm

or

r = 0.3338 mm

thus

the radius of a piece of copper wire in mm = 0.3338 mm (with 4 significant figures)

and

the diameter of a piece of copper wire in mm = 0.3338 mm / 2 = 0.6676 mm

(You have exchanged the values while putting the values in the answer box, please correct it)

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