SOLUTION: Hi. Here is the problem I need help on: Suppose the largest square peg possible is placed in a circular hole and that the largest circular peg possible is placed in a square ho

Algebra ->  Absolute-value -> SOLUTION: Hi. Here is the problem I need help on: Suppose the largest square peg possible is placed in a circular hole and that the largest circular peg possible is placed in a square ho      Log On


   



Question 33855: Hi. Here is the problem I need help on:
Suppose the largest square peg possible is placed in a circular hole and that the largest circular peg possible is placed in a square hole. In which case is there a smaller percentage of space wasted?
Thanks!

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
WHEN A CIRCLE IS INSIDE A SQUARE ,WE HAVE
A=SIDE OF SQUARE =DIAMETER OF CIRCLE
AREA OF SQUARE=A^2
AREA OF CIRCLE =PI*D^2/4=(A^2)(PI/4)
% SPACE LOST =100*A^2{1-(PI/4)}/A^2=100*(1-PI/4)
WHEN A SQUARE IS INSIDE CIRCLE..DIAMETER OF CIRCLE =D=DIAGONAL OF SQUARE =A*SQRT.(2)
AREA OF SQUARE =A^2
AREA OF CIRCLE =PI*D^2/4=PI*A^2*2/4=A^2*(PI/2)
% SPACE LOST =100A^2{(PI/2)-1}/{(A^2)(PI/2)=100{1-(2/PI)}
SINCE (1-PI/4)<{1-(2/PI)}....LESS % OF SPACE IS LOST IF WE PUT A CIRCLE IN A SQUARE.