SOLUTION: a cylindrical log of radius 60 cm and 800 cm long is to be cut to form a wood with square cross section.find the largest volume of the wood that can be obtained.express the volume

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Question 608997: a cylindrical log of radius 60 cm and 800 cm long is to be cut to form a wood with square cross section.find the largest volume of the wood that can be obtained.express the volume in cubic meters.please solve to help.
Answer by ankor@dixie-net.com(22740) (Show Source):
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a cylindrical log of radius 60 cm and 800 cm long is to be cut to form a wood with square cross section.find the largest volume of the wood that can be obtained.
express the volume in cubic meters.
:
The diagonal of the square board obtained is equal to the diameter of the log
diameter = 120 cm
Convert to meters, 1.2 m diameter by 8 m long
Using pytha: a^2 + b^2 = c^2
call both sides a; 2a^2 = c^2
let a = length of the side of the square cross section in meters
let c = diameter of the log
2a^2 = 1.2^2
2a^2 = 1.44
a^2 = .72
then the volume of the board will be
.72 * 8 = 5.72 cu meters