Subjects geometry

Surface Area Cost

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Surface Area Cost


1. **State the problem:** We have a rectangular prism storage container with dimensions 7 m, 5 m, and 2 m. The total cost of the sheet steel used for the surface area is 4484. We need to find the cost per square meter of the sheet steel. 2. **Calculate the surface area of the rectangular prism:** The surface area $SA$ of a rectangular prism with length $l$, width $w$, and height $h$ is given by: $$SA = 2(lw + lh + wh)$$ Substitute $l=7$, $w=5$, and $h=2$: $$SA = 2(7 \times 5 + 7 \times 2 + 5 \times 2)$$ $$SA = 2(35 + 14 + 10)$$ $$SA = 2(59) = 118 \text{ square meters}$$ 3. **Find the cost per square meter:** Total cost = 4484 Cost per square meter $C$ is: $$C = \frac{\text{Total cost}}{\text{Surface area}} = \frac{4484}{118}$$ Calculate: $$C = 38$$ 4. **Final answer:** The sheet steel cost 38 per square meter.