Final answer:
The density of the standard kilogram, a platinum-iridium cylinder with dimensions 39mm x 39mm, is calculated to be 21,276 kg/m³ using the formula ρ = mass/volume after converting dimensions to meters and calculating the volume.
Step-by-step explanation:
The density of a substance is defined as its mass per unit volume. Given that a standard kilogram is a platinum-iridium cylinder with a mass of 1 kg and dimensions 39mm in height by 39mm in diameter, we can calculate its density by first finding its volume. To find the volume of a cylinder, we use the formula πr²h, where π is Pi (approximately 3.14159), r is the radius (half of the diameter), and h is the height.
The density ρ (rho) is calculated by the formula ρ = mass/volume. In this case, the mass is 1 kg (since it's the standard kilogram), and the volume needs to be calculated in cubic meters to match the desired SI units for density kg/m³.
First, we convert the measurements from millimeters to meters (since 1 m = 1000 mm): Height = 0.039 m and Diameter = 0.039 m, thus Radius = 0.0195 m. We then calculate the volume: Volume = π * (0.0195 m)² * 0.039 m = 4.7 x 10⁻µ m³. Finally, we find the density by dividing the mass by the volume: Density = 1 kg / 4.7 x 10⁻µ m³ = 21,276 kg/m³.