Subjects geometry

Volume Stepped Prism 5893C0

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1. **State the problem:** We need to find the volume of a stepped compound rectangular prism with given dimensions. 2. **Understand the shape:** The figure is composed of two rectangular prisms stacked or joined in a stepped manner. 3. **Identify dimensions:** From the image description: - Larger base prism: length = 14 yd, width = 4 yd, height = 3 yd - Smaller top prism: length = 11 yd, width = 3 yd, height = 3 yd 4. **Volume formula for a rectangular prism:** $$V = \text{length} \times \text{width} \times \text{height}$$ 5. **Calculate volume of larger prism:** $$V_1 = 14 \times 4 \times 3 = 168 \text{ cubic yards}$$ 6. **Calculate volume of smaller prism:** $$V_2 = 11 \times 3 \times 3 = 99 \text{ cubic yards}$$ 7. **Total volume:** $$V = V_1 + V_2 = 168 + 99 = 267 \text{ cubic yards}$$ **Final answer:** The volume of the stepped compound rectangular prism is **267 cubic yards**.
14 yd4 yd11 yd3 yd3 yd