Silver metal has a density of 10.5 g/cm3. A solid sphere of silver has a mass of 0.285 g. What is the diameter of the silver piece, in mm?

Question

Answer 1

Elle

Three steps here. First we find the volume of the sphere, then using that and the volume formula we find r. Knowing r we can find the diameter.

The sphere has mass 0.285 g, and 1cm³ has mass 10.5 g.

So mass = Volume x density. so Volume = mass / density = 0.285 / 10.5 (no calculation here, we keep things as exact values).

So we know (4/3) πr³ = (0.285 / 10.5)

So πr³=(0.285 / 10.5) * (3/4)

So r³= (0.285 / 10.5) * (3/4) * (1/3.14). I am assuming π=3.14

Then r is the cube root of this.

And then knowing r, we just double it to get the diameter.

So the calculation gives : 0.372928626 mm as the diameter.

Your initial measurements are given to 3 significant figures, so you should do the same in the answer, giving 0.373 mm.

Couple of notes.

1. To find the cube root , you can just raise your calculated number to the power (1/3).
2. If your calculator has an exact value of π, use that rather than the 3.14 approximation.