Step 1: Calculate the Radius
The diameter of the ball is given as 4.2 cm. The radius \( r \) is half of the diameter: \[ r = \frac{4.2}{2} = 2.1 \, \text{cm} \]
Step 2: Formula for the Volume of a Sphere
The volume \( V \) of a sphere is given by the formula: \[ V = \frac{4}{3} \pi r^3 \] Substituting \( r = 2.1 \, \text{cm} \): \[ V = \frac{4}{3} \pi (2.1)^3 \] First, calculate \( (2.1)^3 \): \[ (2.1)^3 = 9.261 \] Now calculate the volume: \[ V = \frac{4}{3} \times 3.1416 \times 9.261 \approx 38.795 \, \text{cm}^3 \]
Step 3: Calculate the Mass
The mass \( m \) of the ball is given by the formula: \[ m = \text{density} \times \text{volume} \] The density is given as 8.9 g/cm³, and the volume is approximately 38.795 cm³. Substituting these values: \[ m = 8.9 \times 38.795 \approx 345.68 \, \text{g} \]
The mass of the ball is approximately \( 345.68 \, \text{g} \).