Question

What is the length (in cm) of an edge of a cube of gold (density = 19.3 g/mL) which has a mass of 19.92 kg?

What is the length (in cm) of an edge of a cube of salt (density = 2.165 g/mL) which has a mass of 20.04 kg?

What is the mass (in g) of a cube of lead (density = 11.3 g/mL) with an edge length of 1.89 cm?

Answer 1

1)

Density of gold = 19.3 g/mL = 19.3 g/cm³

Mass of gold = 19.92 kg = 19.92 x 10³ g

Volume of gold = mass of gold / Density of gold = (19.92 x 10³ g )/(19.3 g/cm³)

= 1032.12 cm³

Volume of gold cube = 1032.12 cm³

We know that Volume of gold cube = (Length of the edge)³ = 1032.12 cm³

Length of the edge = (1032.12 cm³)^1/3 = 10.15 cm (Ans)

2)

Density of salt = 2.165 g/mL =2.165 g/cm³

Mass of salt = 20.04 kg = 20.04 x 10³ g

Volume of salt = mass of salt / Density of salt = (20.04 x 10³ g )/(2.165  g/cm³)

= 9256.35 cm³

Volume of salt cube = 9256.35 cm³

We know that Volume of gold cube = (Length of the edge)³ = 9256.35 cm³

Length of the edge = (9256.35 cm³)^1/3 = 20.996 cm (Ans)

3)

Length of edge of cube = 1.89 cm

Volume of cube = (Length of edge of cube)³ = (1.89 cm)³ = 6.75 cm³

Density of lead cube = 11.3 g/mL = 11.3 g/cm³

Mass of lead cube = density x volume = 11.3 g/cm³ x 6.75 cm³ = 76.29 g (Ans)