Subjects algebra

Cement Cost

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Cement Cost


1. **State the problem:** We need to find the cost of the cement used to cover the interior floor and walls of a basement room measuring 10m by 18m with a height of 3m, where the cement layer thickness is 5cm. Cement costs 108 per cubic meter. 2. **Convert thickness to meters:** The thickness is 5cm which equals $\frac{5}{100} = 0.05$ meters. 3. **Calculate the volume of cement for the floor:** - Floor area: $10 \times 18 = 180$ m\(^2$) - Volume on floor: $180 \times 0.05 = 9$ m\(^3$) 4. **Calculate the volume of cement for the walls:** - Walls dimensions: Two walls are 10m long and two walls are 18m long, all 3m tall. - Total wall surface area: $2 \times 10 \times 3 + 2 \times 18 \times 3 = 60 + 108 = 168$ m\(^2$) - Volume on walls: $168 \times 0.05 = 8.4$ m\(^3$) 5. **Calculate total volume of cement:** $$9 + 8.4 = 17.4\text{ m}^3$$ 6. **Calculate total cost:** $$17.4 \times 108 = 1879.2$$ **Final answer:** The approximate cost of the cement is 1879.2.