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Solid Geometry Solutions

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Find the volume and total area of the largest cube of wood that can be cut from a log of circular cross-section whose radius is 12.7 inches.

$$V_{cube} = s^3$$

$$TSA_{cube} = 6s^2$$

$$s^2 + s^2 = (2(12.7))^2$$

$$2s^2 = (25.4)^2$$

$$s =\frac {(25.4)}{\sqrt{2}}$$

$$Vol_{cube} =(\frac {(25.4)}{\sqrt{2}})^3$$

$$Vol_{cube} =5793.70 in^3$$

$$TSA_{cube} = 6(\frac {(25.4)}{\sqrt{2}})^2$$

$$TSA_{cube} =1935.16 in^2$$