Question

a silver wire (density = 10.5 ) has a diameter of 0.20 mm. if a sample of this silver wire has a mass of 21 g, how long is this wire?

Answer 1

• The length of the wire is 1591 cm

Since the unit of the density isn't given, I'll assume it to be g/cm³. It's still the same process, except maybe conversion of units.

If the density is 10.5 g/cm³. We know that formula for density is given as mass/volume.

We are given the mass from the question. But we don't have the volume. What we will do is use the density to get the volume. Basically,

• Density = Mass/Volume

1. 10.5 = 21/v
2. v = 21/10.5
3. v = 2 cm³

Given that the volume is 2 cm³, we will proceed to finding the area of the wire.

Area is given as πr². Where r = d/2. Also, d is in mm, so we convert to cm. d = 0.02 cm.

1. Area = 3.142 * 0.02²
2. Area = 0.001257 cm²

• Volume = Area * Length.

Essentially,

1. Length = Volume/Area
2. Length = 2/0.001257
3. Length = 1591 cm

Therefore, the length of the wire is 1591 cm.

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