1. **Problem Statement:** Find the volume and surface area of an L-shaped prism composed of two rectangular prisms joined at one end. 2. **Given Dimensions:** - First prism: length $=10$ in, width $=3$ in, height $=3$ in - Second prism (on top at one end): length $=3$ in, width $=2$ in, height $=6$ in - The width $3$ in is common along the junction. 3. **Volume Calculation:** The total volume is the sum of the volumes of the two prisms. Volume of first prism: $$V_1 = \text{length} \times \text{width} \times \text{height} = 10 \times 3 \times 3 = 90$$ Volume of second prism: $$V_2 = 3 \times 2 \times 6 = 36$$ Total volume: $$V = V_1 + V_2 = 90 + 36 = 126$$ cubic inches 4. **Surface Area Calculation:** Calculate the surface area of each prism separately, then subtract the area of the overlapping face (the junction) because it is counted twice. Surface area of first prism: $$SA_1 = 2(lw + lh + wh) = 2(10 \times 3 + 10 \times 3 + 3 \times 3) = 2(30 + 30 + 9) = 2 \times 69 = 138$$ Surface area of second prism: $$SA_2 = 2(3 \times 2 + 3 \times 6 + 2 \times 6) = 2(6 + 18 + 12) = 2 \times 36 = 72$$ Area of overlapping face (junction): The overlapping face is the bottom of the second prism and top of the first prism where they meet. Its dimensions are length $=3$ in and width $=2$ in. $$A_{overlap} = 3 \times 2 = 6$$ Total surface area: $$SA = SA_1 + SA_2 - 2 \times A_{overlap} = 138 + 72 - 2 \times 6 = 210 - 12 = 198$$ square inches 5. **Final answers:** - Volume $= 126$ cubic inches - Surface area $= 198$ square inches