Subjects geometry

Ornament Volume C4D007

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1. **State the problem:** Krystal wants to fill 6 spherical ornaments with glitter. Each ornament is a sphere with a diameter of 3 inches. We need to find the total volume of glitter required to fill all 6 ornaments. 2. **Formula for the volume of a sphere:** $$V = \frac{4}{3} \pi r^3$$ where $r$ is the radius of the sphere. 3. **Calculate the radius:** The diameter is 3 inches, so the radius is: $$r = \frac{3}{2} = 1.5 \text{ inches}$$ 4. **Calculate the volume of one ornament:** Using $\pi = 3$ as given, $$V = \frac{4}{3} \times 3 \times (1.5)^3$$ 5. **Simplify the expression:** $$V = \cancel{\frac{4}{3}} \times \cancel{3} \times (1.5)^3 = 4 \times (1.5)^3$$ 6. **Calculate $1.5^3$:** $$1.5^3 = 1.5 \times 1.5 \times 1.5 = 3.375$$ 7. **Calculate the volume of one ornament:** $$V = 4 \times 3.375 = 13.5 \text{ cubic inches}$$ 8. **Calculate the total volume for 6 ornaments:** $$6 \times 13.5 = 81 \text{ cubic inches}$$ **Final answer:** Krystal needs **81 cubic inches** of glitter to fill all 6 ornaments.