A iron wire (density = 7.86 g/cm^3) has a diameter of 0.0518cm. What is the mass, in grams, of a 9.49 in length of this wire?

Question

consider volume of a cylinder

Answer 1

Since density is mass/volume, we need to determine the volume of wire so we can then determine the mass.

Considering the wire as a cylinder, the volume is given by V = π r² h and since we want the volume to be in cm³, we want to use units of cm. The radius r will thus be 0.0518 cm/2 = 0.0259 cm. The height (h) will be 9.49 inches x 2.54 cm/inch = 24.1 cm. So, volume (V) = (3.1416)(0.0259 cm)²(24.1 cm) = 0.0509 cm³

Now to find the mass, we use the given density of 7.86 g/cm^3.

0.0509 cm³ x 7.86 g/cm³ = 0.39998 g = 0.400 g (to 3 sig. figs.)