1. **State the problem:** We need to complete the table of volumes of spheres for given radii and determine if the relationship between radius and volume is linear. 2. **Formula for volume of a sphere:** $$V = \frac{4}{3} \pi r^3$$ where $V$ is the volume and $r$ is the radius. 3. **Calculate volumes for each radius:** - For $r=1$: $$V = \frac{4}{3} \pi (1)^3 = \frac{4}{3} \pi \approx 4.2$$ - For $r=2$: $$V = \frac{4}{3} \pi (2)^3 = \frac{4}{3} \pi (8) = \frac{32}{3} \pi \approx 33.5$$ - For $r=3$: $$V = \frac{4}{3} \pi (3)^3 = \frac{4}{3} \pi (27) = 36 \pi \approx 113.1$$ - For $r=4$: $$V = \frac{4}{3} \pi (4)^3 = \frac{4}{3} \pi (64) = \frac{256}{3} \pi \approx 268.1$$ 4. **Complete the table:** | Radius (cm) | Volume of Sphere (cm³) | |-------------|------------------------| | 1 | $\frac{4}{3} \pi$ or 4.2 | | 2 | $\frac{32}{3} \pi$ or 33.5 | | 3 | $36 \pi$ or 113.1 | | 4 | $\frac{256}{3} \pi$ or 268.1 | 5. **Is the relationship linear?** The volume depends on the cube of the radius ($r^3$), so the relationship between radius and volume is **not linear**. As radius increases, volume increases much faster (cubically). **Final answer:** - Volumes: $\frac{4}{3} \pi$, $\frac{32}{3} \pi$, $36 \pi$, $\frac{256}{3} \pi$ or approximately 4.2, 33.5, 113.1, 268.1 cm³ respectively. - Relationship is not linear.