document.write( "Question 1204501: What is the maximum number of bottles, each of diameter 10 cm, that can be packed into a box with a square base measuring 1000 cm by 1000 cm? The diagram below shows the closest packing method. \r
\n" ); document.write( "\n" ); document.write( "https://ibb.co/KqVSGkL\r
\n" ); document.write( "\n" ); document.write( "i understand Honorable Tutor User Ikelyn has already posted some similar problem but i didnt get it so can u pls just post the solution thx \n" ); document.write( "
Algebra.Com's Answer #841020 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
\r\n" );
document.write( "The circles are the bottoms of the bottles.  The left front corner looks like\r\n" );
document.write( "this.  We are looking down upon the bottles in the box.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "There are 100 bottles on the 1st row, 99 on the 2nd row, 100 on the 3rd row, \r\n" );
document.write( "etc.  So between the front side of the box and the green line, there are 299 \r\n" );
document.write( "bottles.\r\n" );
document.write( "\r\n" );
document.write( "The two red triangles are 30-60-90 right triangles, each with vertical sides \r\n" );
document.write( "\"5sqrt%283%29\".  It's 2 more radii (one diameter) from the side of the box to\r\n" );
document.write( "the green line, so the distance from the side of the box to the green line is \r\n" );
document.write( "\"10%2B10sqrt%283%29=%2227.3%2B%22\" cm.  We divide that into 1000 and get 36.6+.  \r\n" );
document.write( "\r\n" );
document.write( "So 36 times 299 bottles gives us 10764 bottles up to \"36%2810%2B10sqrt%283%29%29=%22983.5%2B%22\" cm.\r\n" );
document.write( "So there are \"1000-%22983.5%2B%22\" or about 16.5 cm. left from the green line\r\n" );
document.write( "to the left back side of the box.\r\n" );
document.write( "\r\n" );
document.write( " \r\n" );
document.write( "\r\n" );
document.write( "So there is only room enough for 1 more row of 99 bottles, or 10764+99=10863\r\n" );
document.write( "bottles.  But if they didn't have to each have their centers 60o apart, \r\n" );
document.write( "we could easily squeeze in a few more bottles. Maybe another tutor will do a\r\n" );
document.write( "better job that I have here.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\n" ); document.write( "
\n" );