1. **State the problem:** We need to find the mass of a solid gold sphere with radius $r=7$ cm, given the density of gold is $0.019$ kg/cm³. 2. **Formula for volume of a sphere:** The volume $V$ of a sphere is given by $$V=\frac{4}{3}\pi r^3$$ where $r$ is the radius. 3. **Calculate the volume:** Substitute $r=7$ cm into the formula: $$V=\frac{4}{3}\pi (7)^3=\frac{4}{3}\pi \times 343=\frac{4}{3} \times 3.1416 \times 343$$ $$V \approx 4.1888 \times 343 = 1436.76 \text{ cm}^3$$ 4. **Calculate the mass:** Mass $m$ is density $\times$ volume: $$m = 0.019 \times 1436.76 = 27.29844 \text{ kg}$$ 5. **Round the answer:** To 1 decimal place, $$m \approx 27.3 \text{ kg}$$ **Final answer:** The mass of the gold sphere is approximately **27.3 kg**.