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Difference between revisions of "2005 AMC 12B Problems/Problem 5"
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== Problem ==
 
== Problem ==
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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 $8$-foot by $10$-foot floor is tiles with square tiles of size $1$ foot by $1$ foot. Each tile has a pattern consisting of four white quarter circles of radius $1/2$ 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]

$\mathrm{(A)}\ 80-20\pi \qquad \mathrm{(B)}\ 60-10\pi \qquad \mathrm{(C)}\ 80-10\pi \qquad \mathrm{(D)}\ 60+10\pi \qquad \mathrm{(E)}\ 80+10\pi$

Solution

See also

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