2005 AMC 12B Problems/Problem 5: Difference between revisions
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== Problem == | == Problem == | ||
An <math>8</math>-foot by <math>10</math>-foot floor is tiles with square tiles of size <math>1</math> foot by <math>1</math> foot. Each tile has a pattern consisting of four white quarter circles of radius <math>1/2</math> foot centered at each corner of the tile. The remaining portion of the tile is shaded. How many square feet of the floor are shaded? | |||
<asy> | |||
unitsize(2cm); | |||
defaultpen(linewidth(.8pt)); | |||
fill(unitsquare,gray); | |||
filldraw(Arc((0,0),.5,0,90)--(0,0)--cycle,white,black); | |||
filldraw(Arc((1,0),.5,90,180)--(1,0)--cycle,white,black); | |||
filldraw(Arc((1,1),.5,180,270)--(1,1)--cycle,white,black); | |||
filldraw(Arc((0,1),.5,270,360)--(0,1)--cycle,white,black); | |||
</asy> | |||
<math> | |||
\mathrm{(A)}\ 80-20\pi \qquad | |||
\mathrm{(B)}\ 60-10\pi \qquad | |||
\mathrm{(C)}\ 80-10\pi \qquad | |||
\mathrm{(D)}\ 60+10\pi \qquad | |||
\mathrm{(E)}\ 80+10\pi | |||
</math> | |||
== Solution == | == Solution == | ||
Revision as of 21:23, 17 April 2009
Problem
An 
-foot by 
-foot floor is tiles with square tiles of size 
foot by foot. Each tile has a pattern consisting of four white quarter circles of radius 
foot centered at each corner of the tile. The remaining portion of the tile is shaded. How many square feet of the floor are shaded?
![[asy] unitsize(2cm); defaultpen(linewidth(.8pt)); fill(unitsquare,gray); filldraw(Arc((0,0),.5,0,90)--(0,0)--cycle,white,black); filldraw(Arc((1,0),.5,90,180)--(1,0)--cycle,white,black); filldraw(Arc((1,1),.5,180,270)--(1,1)--cycle,white,black); filldraw(Arc((0,1),.5,270,360)--(0,1)--cycle,white,black); [/asy]](http://latex.artofproblemsolving.com/c/b/e/cbe2bb4966beb1c1cbc889938c8e120b7d80639b.png)
