The density of chromium metal is 7.14 g/cm3. A cube of chromium has a mass of 20.00 kilograms. Calculate the length of each side of the cube in inches.

Answer 1

20.00kg X 1000g/kg this converts the block to grams=20000.00 grams

20000 g X 1cm³/7.14g this will convert the answer to cm³ = 2801.12

Take the cube root of 2801.12 and express the answer to 3 sig figs since 7.14 has three sig figs and is the smallest sig fig factor. =14.1 cm is the length of each side. in cm

multiply 14.1 X 1 in/2.54 cm this will convert to inches= 5.55 inches per side

Answer 2

Density = Mass/volume and Volume of a cube is the cube of the side length. Let s = side length, V = volume, ρ = density and m = mass. Then ρ = m/V = m/s³ or s = cube root(m/ρ).

To work the problem, we need to get things in compatible units so lets put the mass into grams. 20 kg x 1000g/kg = 20,000 g

So, s = cube root (20,000/7.14) = 14.096 cm but since the givens have at most 3 sig figs, we round to 14.1 cm