1. **State the problem:** We have a right rectangular prism with a shaded part inside it. The volume of the shaded part is 102 in³. We are asked to find the volume of the entire right rectangular prism. 2. **Recall the formula for volume of a right rectangular prism:** $$\text{Volume} = \text{length} \times \text{width} \times \text{height}$$ 3. **Analyze the given information:** - The shaded part is inside the prism and has volume 102 in³. - One dimension of the prism is given as 6 in. 4. **Reasoning:** Since the shaded part is inside the prism, its volume is less than or equal to the volume of the entire prism. 5. **Assuming the shaded part shares the same height (6 in) as the prism:** Let the base area of the shaded part be $A_s$ and the base area of the entire prism be $A_p$. 6. **Volume of shaded part:** $$102 = A_s \times 6$$ 7. **Solve for $A_s$:** $$A_s = \frac{102}{6} = 17$$ 8. **Since the shaded part is a portion of the base, and the prism's base area is larger, the volume of the prism is:** $$\text{Volume of prism} = A_p \times 6$$ 9. **If the shaded part is exactly the base of the prism, then the volume of the prism is 102 in³. But since the shaded part is only a portion, the prism's volume is larger. Without more information about the base dimensions, we cannot find the exact volume.** **However, if the shaded part is the entire base, then the volume of the prism is:** $$102 \text{ in}^3$$ **If the shaded part is a fraction of the base, the volume is larger accordingly.** **Final answer:** The volume of the right rectangular prism is greater than or equal to 102 in³, depending on the base dimensions. Since the problem states the shaded part volume is 102 in³ and the prism height is 6 in, the volume of the prism is: $$\text{Volume} = \text{Base area} \times 6 = \frac{102}{6} \times 6 = 102$$ So the volume of the prism is 102 in³ if the shaded part is the entire base.