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

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) (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.
RELATED QUESTIONS
I have 2 drawings. One has a circle inscribed in a square(round peg in square hole). The... (answered by vleith,stanbon)

Pls answer it imeediately because i need the answer as soon as possible, Thanks... (answered by stanbon)

I am attempting to help my daughter with her Algebra 2 homework. I got the problem set... (answered by Fombitz)

If you cut out the largest possible circular pie crust for a square piece of dough that... (answered by mananth)

hi my names jessie, im doing homework rite now and i need someones help here is the... (answered by josmiceli,ohtheirony)

Last night it started raining as Hibah was closing up the store where she works. By 3 am, (answered by ikleyn)

Hi, I need help on a problem. My problem is to see what are the intercepts of the points (answered by Alan3354)

Hi, Can you please explain how to solve this problem? I have a paper plate with radius... (answered by rfer)

Briana's backyard is a square that measures 20 feet on each side. She wants to plant the... (answered by katealdridge)