1. **State the problem:** We need to find the volume of a sphere with radius $r = 2.7$ cm, rounded to the nearest cubic centimeter. 2. **Formula for the volume of a sphere:** $$V = \frac{4}{3} \pi r^3$$ 3. **Substitute the radius into the formula:** $$V = \frac{4}{3} \pi (2.7)^3$$ 4. **Calculate the cube of the radius:** $$2.7^3 = 2.7 \times 2.7 \times 2.7 = 19.683$$ 5. **Calculate the volume:** $$V = \frac{4}{3} \pi \times 19.683$$ 6. **Multiply constants:** $$V = \frac{4}{3} \times 3.1416 \times 19.683$$ 7. **Calculate step-by-step:** $$\frac{4}{3} \times 3.1416 = 4.1888$$ $$V = 4.1888 \times 19.683 = 82.466$$ 8. **Round to the nearest cubic centimeter:** $$V \approx 82$$ **Final answer:** The volume of the sphere is approximately **82 cubic centimeters**.