Question

A kidnapper demands a 42 kg cube of platinum as a ransom. What is the length of a side?

Answer 1

To calculate the side length of the 42 kg platinum cube, we find the cube root of the volume, which is the mass divided by the density of platinum. The result is approximately 12.5 cm for each side of the cube.

Step-by-step explanation:

To find the length of a side of a cube of platinum with a mass of 42 kg, we need to use the formula for the volume of a cube (V = s³, where s is the length of a side) and the relationship between mass, volume, and density (mass = density × volume).

First, we find the density of platinum, which is approximately 21,450 kg/m³. Using the mass of the platinum cube (42 kg), we calculate the volume:

Volume = Mass / Density = 42 kg / 21,450 kg/m³ ≈ 0.001958 m³.

Now, to find a side length, we take the cube root of the volume:

Side length = √³(Volume) = √³(0.001958 m³) ≈ 0.125 m or 12.5 cm.

Therefore, the kidnapper is demanding a cube of platinum with each side being approximately 12.5 cm long.

Answer 2

To find the length of a side (s) of a cube, you can use the formula: Volume of cube = s³. The length of a side of the platinum cube with the mass 42 kg is approximately 0.127 m or 12.7 cm.

Step-by-step explanation:

To find the length of a side (s) of a cube, you can use the formula:

Volume of cube = s³

The volume of the cube is the mass (m) of the platinum cube divided by its density (ρ):

Volume of cube =
`(m)/(\rho)`

Platinum has a density of approximately 21,450 kg/m³.

So, the formula becomes:

s³ =
`(m)/(\rho)`

Plug in the values:

s³ =
`\frac{42 \, \text{kg}}{21,450 \, \text{kg/m}^3}`

Now, solve for s:

s³ ≈ 0.001955

s ≈ ∛0.001955

s ≈ 0.127 m

So, the length of a side of the platinum cube is approximately 0.127 m or 12.7 cm.