1. **Problem Statement:** Calculate the volume (متره) and estimate the cost (براورد) of a floor slab made of تیرچه و یونولیت (joist and polystyrene) with a thickness of 30 cm, excluding the cost of steel reinforcement (میلگرد). The floor plan consists of a grid with beams spaced 440 cm and 600 cm horizontally, and 400 cm and 340 cm vertically. Beam width is 40 cm. 2. **Step 1: Calculate the total floor area.** The floor is divided into two rows and three columns of rectangular sections. Horizontal lengths: $440 + 600 = 1040$ cm Vertical lengths: $400 + 340 = 740$ cm Convert to meters: $$ \text{Length} = \frac{1040}{100} = 10.4\,m $$ $$ \text{Width} = \frac{740}{100} = 7.4\,m $$ Total floor area: $$ A = 10.4 \times 7.4 = 76.96\,m^2 $$ 3. **Step 2: Calculate the volume of the slab.** Thickness is 30 cm = 0.3 m. Volume: $$ V = A \times \text{thickness} = 76.96 \times 0.3 = 23.088\,m^3 $$ 4. **Step 3: Calculate the volume of beams.** Beams run along the grid lines. There are 3 vertical beams and 3 horizontal beams. Vertical beams length: $$ 3 \times 7.4 = 22.2\,m $$ Horizontal beams length: $$ 3 \times 10.4 = 31.2\,m $$ Total beam length: $$ L = 22.2 + 31.2 = 53.4\,m $$ Beam cross-section area: $$ 0.4\,m \times 0.3\,m = 0.12\,m^2 $$ Beam volume: $$ V_b = L \times 0.12 = 53.4 \times 0.12 = 6.408\,m^3 $$ 5. **Step 4: Calculate the volume of the joist and polystyrene slab excluding beams.** Slab volume excluding beams: $$ V_s = V - V_b = 23.088 - 6.408 = 16.68\,m^3 $$ 6. **Step 5: Summary** - Total slab volume (including beams): $23.088\,m^3$ - Beam volume: $6.408\,m^3$ - Joist and polystyrene volume: $16.68\,m^3$ 7. **Step 6: Cost estimation** To estimate cost, multiply volumes by unit prices of materials (not provided). --- **Final answer:** Total volume of slab including beams is **23.088 cubic meters**. Beam volume is **6.408 cubic meters**. Joist and polystyrene volume is **16.68 cubic meters**. These volumes can be used for material quantity estimation and cost calculation excluding steel reinforcement.