Just out of curiosity, how did you derive d = a * sqrt(2)? Were you given that formula?
Kern & Bland solid mensuration page 20 number 6
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.
I know 12.7 in is the radius and is also half the diagonal of the square (25.4 in)
I also know d = a sqrt2 and since I know d is 25.4 I can calculate a as 25.4 divided by sqrt 2
which is 17.9605 in.
I know Volume is a3
and total area is 6a2
and the answer on the book is in ft. so I'd have to divide by 12 so I'd get 1.4957 ft.
answer should be 3.3528 cu. ft and 13.441 sq. ft.
is this right?