Subjects geometry

Rectangular Pyramid 2A94F6

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1. **State the problem:** Find the volume of a rectangular pyramid with base length 12 inches, base width 10 inches, and height 8 inches. 2. **Formula:** The volume $V$ of a pyramid is given by $$V = \frac{1}{3} \times \text{Base Area} \times \text{Height}$$ where the base area for a rectangular base is $$\text{Base Area} = \text{length} \times \text{width}$$ 3. **Calculate the base area:** $$\text{Base Area} = 12 \times 10 = 120$$ square inches. 4. **Calculate the volume:** $$V = \frac{1}{3} \times 120 \times 8$$ 5. **Simplify the multiplication:** $$V = \frac{1}{3} \times 960$$ 6. **Simplify the fraction:** $$V = \cancel{\frac{1}{3}} \times \cancel{960}$$ Since $960 \div 3 = 320$, we have $$V = 320$$ cubic inches. **Final answer:** The volume of the rectangular pyramid is $320$ cubic inches.