Subjects geometry

Pyramid Volume C99Bbf

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1. The problem asks for the volume of a right rectangular pyramid with base length 12 feet, base width 9 feet, and height 18 feet. 2. The formula for the volume $V$ of a right rectangular pyramid is: $$V = \frac{1}{3} \times \text{base area} \times \text{height}$$ where the base area for a rectangle is: $$\text{base area} = \text{length} \times \text{width}$$ 3. Calculate the base area: $$12 \times 9 = 108 \text{ square feet}$$ 4. Substitute the base area and height into the volume formula: $$V = \frac{1}{3} \times 108 \times 18$$ 5. Simplify the multiplication: $$108 \times 18 = 1944$$ 6. Now divide by 3: $$\frac{1944}{3} = 648$$ 7. Therefore, the volume of the pyramid is: $$\boxed{648}$$ cubic feet. This corresponds to answer choice B.