Subjects geometry

I Shape Volume

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1. **State the problem:** We need to find the volume of a 3D solid shaped like a large "I". It consists of three rectangular parts: two horizontal parts (top and bottom) and one vertical middle section. 2. **Identify dimensions:** - Top and bottom parts: length = 6 in, height = 2 in, depth = 2 in - Middle vertical section: height = 7 in, width = 3 in, depth = 2 in 3. **Formula for volume of a rectangular prism:** $$\text{Volume} = \text{length} \times \text{width} \times \text{height}$$ 4. **Calculate volume of top part:** $$V_{top} = 6 \times 2 \times 2 = 24 \text{ in}^3$$ 5. **Calculate volume of bottom part:** $$V_{bottom} = 6 \times 2 \times 2 = 24 \text{ in}^3$$ 6. **Calculate volume of middle section:** $$V_{middle} = 3 \times 2 \times 7 = 42 \text{ in}^3$$ 7. **Add volumes to get total volume:** $$V_{total} = V_{top} + V_{middle} + V_{bottom} = 24 + 42 + 24 = 90 \text{ in}^3$$ **Final answer:** The volume of the "I" shaped solid is **90 in³**.