document.write( "Question 14983: You have two boxes of the same shape that hold flour. The larger box holds twice as much flour as the smaller one. You conclude that it would take you ?? times as much paint to paint the lager box then it would take you to paint the smaller box. \n" ); document.write( "

Algebra.Com's Answer #7443 by rapaljer(4671) $\"\"$ $\"About$

You can put this solution on YOUR website!
Let V = volume of the smaller box. Since $\"+V=+x%5E3\"$ , where x is the length of the side of each square side, each side of this box will be $\"x+=+root%283%2CV%29\"$ , and the area of each face of the box will be $\"A+=+x%5E2+=+%28root%283%2CV%29%29%5E2+=+V%5E%282%2F3%29+\"$ .\r
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\n" ); document.write( "\n" ); document.write( "Now, the larger box has twice the volume or 2V, where $\"+2V=+y%5E3\"$ , where y is the length of the side of each square side. Each side of this box will be $\"y+=+root%283%2C%282V%29%29\"$ , and the area of each face of the box will be

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\n" ); document.write( "\n" ); document.write( "Notice that the larger box has area of each face that is similar to the face of the smaller of the box, except that it is multliplied by $\"2%5E%282%2F3%29+\"$ power. This computes to a surface area that is about 1.587 times as much as the smaller box, so it should take about 1.587 times as long to paint the box. Hey, it's late in Florida right now, and maybe someone will check this out and make sure I'm right!! Any volunteers??\r
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\n" ); document.write( "\n" ); document.write( "R^2 at SCC \n" ); document.write( "

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