1. **Problem (a):** Rectangular prism with length $10$ cm, width $6$ cm, height $8$ cm. - Cross-sectional area (base area) $= \text{length} \times \text{width} = 10 \times 6 = 60$ cm$^2$. - Lateral surface area $= 2 \times \text{height} \times (\text{length} + \text{width}) = 2 \times 8 \times (10 + 6) = 2 \times 8 \times 16 = 256$ cm$^2$. - Total surface area $= 2 \times \text{base area} + \text{lateral surface area} = 2 \times 60 + 256 = 120 + 256 = 376$ cm$^2$. - Volume $= \text{base area} \times \text{height} = 60 \times 8 = 480$ cm$^3$. 2. **Problem (b):** Cube with side length $5$ cm. - Cross-sectional area $= 5 \times 5 = 25$ cm$^2$. - Lateral surface area $= 4 \times (5 \times 5) = 4 \times 25 = 100$ cm$^2$. - Total surface area $= 6 \times (5 \times 5) = 6 \times 25 = 150$ cm$^2$. - Volume $= 5^3 = 125$ cm$^3$. 3. **Problem (ग):** Composite prism with heights $9$ cm and widths $4$, $3$, and $6$ cm forming a combined base. - Cross-sectional area calculated by summing areas $= (4 \times 9) + (3 \times 9) + (6 \times 9) = (36 + 27 + 54) = 117$ cm$^2$. - Lateral surface area includes perimeters times height, assuming heights and widths as sides: Compute perimeter: sum of all distinct edges around the base; here perimeter $= 2(4 + 3 + 6) = 26$ cm. Lateral surface area $= \text{perimeter} \times \text{height} = 26 \times 9 = 234$ cm$^2$. - Total surface area $= 2 \times \text{cross-sectional area} + \text{lateral surface area} = 2 \times 117 + 234 = 234 + 234 = 468$ cm$^2$. - Volume $= \text{cross-sectional area} \times \text{height} = 117 \times 9 = 1053$ cm$^3$. 4. **Problem (घ):** Cross-shaped prism composed of rectangular segments with widths/depths $3$ cm and heights $4$ cm and $8$ cm. - Cross-sectional area is sum of areas: $(3 \times 4) \times 4 + (3 \times 8) \times 3 = (12 \times 4) + (24 \times 3) = 48 + 72 = 120$ cm$^2$. - Lateral surface area approximated as perimeter $\times$ height. Perimeter $= 2 \times (3 + 4 + 3 + 8) = 36$ cm. Height average $= (4 + 8)/2 = 6$ cm. Lateral surface area $= 36 \times 6 = 216$ cm$^2$. - Total surface area $= 2 \times 120 + 216 = 240 + 216 = 456$ cm$^2$. - Volume $= \text{cross-sectional area} \times \text{height average} = 120 \times 6 = 720$ cm$^3$. 5. **Problem (ड):** House-shaped prism with rectangular base $6 \times 4$ cm and triangular prism top with base $6$ cm and height $3$ cm. - Cross-sectional area $= \text{rectangle area} + \text{triangle area} = (6 \times 4) + (0.5 \times 6 \times 3) = 24 + 9 = 33$ cm$^2$. - Lateral surface area $= \text{perimeter of base} \times \text{height} = (2 \times (6 + 4)) \times 3 = 20 \times 3 = 60$ cm$^2$ plus triangle lateral area: For triangular faces (height of prism to side length assumed equal) $= 2 \times (\text{triangle side} \times 3)$ but given limited data, estimate lateral area for triangular part as $6 \times 3 = 18$ cm$^2$. Total lateral surface area $= 60 + 18 = 78$ cm$^2$. - Total surface area $= 2 \times 33 + 78 = 66 + 78 = 144$ cm$^2$. - Volume $= \text{cross-sectional area} \times \text{length/depth} = 33 \times 3 = 99$ cm$^3$. 6. **Problem (च):** Step-shaped prism with step heights and widths $10$ cm and top step width $30$ cm. - Cross-sectional area sum of rectangles: $10 \times 10 + 10 \times 10 + 10 \times 30 = 100 + 100 + 300 = 500$ cm$^2$. - Lateral surface area approximated by summing perimeter times height: Perimeter $= 2 \times (10 + 30) = 80$ cm. Height total $= 10 + 10 + 10 = 30$ cm. Lateral surface area $= 80 \times 30 = 2400$ cm$^2$. - Total surface area $= 2 \times 500 + 2400 = 1000 + 2400 = 3400$ cm$^2$. - Volume $= \text{cross-sectional area} \times \text{depth} = 500 \times 10 = 5000$ cm$^3$. **Final answers:** (a) Cross-sectional area $= 60$ cm$^2$, Lateral surface area $= 256$ cm$^2$, Total surface area $= 376$ cm$^2$, Volume $= 480$ cm$^3$. (b) Cross-sectional area $= 25$ cm$^2$, Lateral surface area $= 100$ cm$^2$, Total surface area $= 150$ cm$^2$, Volume $= 125$ cm$^3$. (ग) Cross-sectional area $= 117$ cm$^2$, Lateral surface area $= 234$ cm$^2$, Total surface area $= 468$ cm$^2$, Volume $= 1053$ cm$^3$. (घ) Cross-sectional area $= 120$ cm$^2$, Lateral surface area $= 216$ cm$^2$, Total surface area $= 456$ cm$^2$, Volume $= 720$ cm$^3$. (ड) Cross-sectional area $= 33$ cm$^2$, Lateral surface area $= 78$ cm$^2$, Total surface area $= 144$ cm$^2$, Volume $= 99$ cm$^3$. (च) Cross-sectional area $= 500$ cm$^2$, Lateral surface area $= 2400$ cm$^2$, Total surface area $= 3400$ cm$^2$, Volume $= 5000$ cm$^3$.