SOLUTION: 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 in. (use ft. as unit)

Question 838943: 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 in. (use ft. as unit)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
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 in. (use ft. as unit)
:
The cube's square side's hypotenuse will be the diameter of the log: 25.4"
Let x = the length of one side
x^2 + x^2 = 25.4^2
2x^2 = 645.16
divide both sides by 2
x^2 = 322.58; the area of one side
x =
x = 17.096 in, one side of the cube
Find the vol of the cube
Vol: 17.096^3 = 5793.7 cu/in
Change to cubic ft (1728 cu/in in one cu ft)
= 3.353 cu/ft
:
Find the total surface area: 6(322.58) = 1935.48 sq/in
Change to sq/ft; (1 sq/ft = 144 sq/in)
= 13.44 sq/ft

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