A sphere of gold with a radius of 14.9 cm. (density \( =19.3 \frac{\mathrm{~g}}{\mathrm{~cm}^{3}} \) ). Round your answer to 3 significant digits. mass: \( \square \mathrm{g} \)

To calculate the mass of a gold sphere with a radius of 14.9 cm and a density of \(19.3 \, \frac{\text{g}}{\text{cm}^3}\), follow these steps: 1. **Calculate the Volume of the Sphere:** The volume \( V \) of a sphere is given by: \[ V = \frac{4}{3} \pi r^3 \] Where \( r = 14.9 \, \text{cm} \). \[ V = \frac{4}{3} \times \pi \times (14.9)^3 \approx 4.18879 \times 3307.949 \approx 13,\!856.3 \, \text{cm}^3 \] 2. **Calculate the Mass:** Mass \( m \) is the product of density \( \rho \) and volume \( V \): \[ m = \rho \times V = 19.3 \, \frac{\text{g}}{\text{cm}^3} \times 13,\!856.3 \, \text{cm}^3 \approx 267,\!000 \, \text{g} \] 3. **Round to Three Significant Digits:** \[ m \approx 2.67 \times 10^5 \, \text{g} \] **Final Answer:** \[ \text{mass} = 2.67 \times 10^{5} \, \mathrm{g} \]