1. **State the problem:** We want to determine if a ball with a volume of 65.42 cm³ can fit inside a sphere with radius 3 cm. 2. **Calculate the volume of the larger sphere:** The volume $V$ of a sphere is given by $$V = \frac{4}{3} \pi r^3$$ where $r$ is the radius. 3. **Substitute the radius:** $$V = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi 27 = 36\pi \approx 113.10 \text{ cm}^3$$ 4. **Compare volumes:** The ball's volume is 65.42 cm³, and the larger sphere's volume is approximately 113.10 cm³. 5. **Conclusion:** Since 65.42 cm³ < 113.10 cm³, the ball can fit inside the sphere.