Problema 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 12.7in.
Answer provided by our tutors
draw the log and the cube inside
let
r = 12.7 in is the radius of the log
a = the length of the side of the cube
d = the diagonal of the cube
the diagonal of the cube d = 2r
using Pythagorean Theorem we have
a^2 + a^2 = d^2
2a^2 = (2*12.7)^2
a^2 = (2*12.7)^2/2
a = 17.96 in
the total area of a cube is A = 6*a^2
A = (6*(2*12.7)^2)/2
A = 1935.48 in^2
the volume of a cube is V = a^3
V = 17.96^3
V = 5793. 21 in^3