Mathematics Notes - Solid Geometry Problems and Solutions

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.

$log of circular cross-section whose radius is 12.7 inches.$

$V_{cube} = s^3$

$TSA_{cube} = 6s^2$

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

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

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

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

$Vol_{cube} =5793.70 in^3$

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

$TSA_{cube} =1935.16 in^2$