Question

Calculate the density of a rod of metal in g/cm3, with a mass of 9.58g, a diameter of 8 mm and a height of 3.5cm

Answer 1

The density of a metal rod can be calculated by dividing its mass by its volume, with the volume computed using the formula for the volume of a cylinder. After converting the diameter to radius, and substituting the values into the volume formula, the rod's density in g/cm³ can be determined.

Step-by-step explanation:

To calculate the density of a metal rod given its mass, diameter, and height, we use the formula for density ρ, which is mass (m) divided by volume (V). The formula is ρ = m/V. The volume of a cylinder (which a rod is mathematically) is given by V = π × r² × h, where 'r' is the radius and 'h' is the height of the cylinder. First, we need to convert the diameter to the radius by dividing it by 2, so the radius is 4 mm or 0.4 cm. The volume of the rod is then calculated using the formula for the volume of a cylinder: V = π × (0.4 cm)² × 3.5 cm.

After finding the volume, we divide the mass of the rod by this volume to get the density. In this case:

1. Convert diameter to radius: r = 8 mm / 2 = 4 mm = 0.4 cm
2. Calculate the volume of the cylinder (rod): V = π × (0.4 cm)² × 3.5 cm
3. Calculate the density: ρ = 9.58 g / V

Proceeding with the calculation will give us the density in g/cm³.

Answer 2

5.448 g/cm³

Step-by-step explanation:

Density: This is defined as the ratio of the mass of a body to its volume.

The unit of density is kg/m³ other sub units are g/cm³, mg/mm³.

From the question,

D = m/πr²h......................... Equation 1

Where D = density, m = mass, r = radius, h = height.

Given: m = 9.58 g, r = 8/2 mm = 4 mm = 0.4 cm, h = 3.5 cm

Substitute this values into equation 1

D = 9.58/(3.14×0.4²×3.5)

D = 5.448 g/cm³

Hence the density of the metal rod is 5.448 g/cm³