document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=53409>Question 53409</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Good evening, i would like to ask you this three problems, i am not sure that i work out the answers. Please, help in those<BR>\n" );
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document.write( "1) A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides?\r<BR>\n" );
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document.write( "2) A regular hexagon is inscribed in a circle o radius R cms. What is the perimeter of the regular hexagon?\r<BR>\n" );
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document.write( "3) A 4cm cube is cut into 1cm cubes. What is the percentage increase in the surface area after such cutting?\r<BR>\n" );
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document.write( "    From yours poor students<BR>\n" );
document.write( "                babynarah and modi </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #35700 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=35700\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) A solid cube of side 6 is first painted pink and then cut into smaller cubes of side 2. How many of the smaller cubes have paint on exactly 2 sides? <BR>\n" );
document.write( "Before cutting the cube is 6^3 cb. units = 216 cu units<BR>\n" );
document.write( "The smaller cubes are 2^3 units or 8 cu units<BR>\n" );
document.write( "Dividing 216 by 8 you get 27 small cubes.<BR>\n" );
document.write( "How many of them have paint on exactly two sides?<BR>\n" );
document.write( "There are four on each edge; so there are 4*6=24 with exactly<BR>\n" );
document.write( "two pink sides.<BR>\n" );
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document.write( "2) A regular hexagon is inscribed in a circle of radius R cms. What is the perimeter of the regular hexagon? <BR>\n" );
document.write( "Draw the picture of the hexagon.<BR>\n" );
document.write( "Draw the 6 radii--one to each of the six vertices.<BR>\n" );
document.write( "Each of the triangles formed is an equilateral triangle.<BR>\n" );
document.write( "So all sides of each triagle are length 6.<BR>\n" );
document.write( "So the perimeter of the hexagon is 6*6= 36 cm\r<BR>\n" );
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document.write( "3) A 4cm cube is cut into 1cm cubes. What is the percentage increase in the surface area after such cutting? <BR>\n" );
document.write( "The surface area of the original cube is 6*4^2=96 cm sq.<BR>\n" );
document.write( "Each of the 1cm cubes has a surface area of 6*1^2=6 cm sq.<BR>\n" );
document.write( "There are 4^3=64 small cubes<BR>\n" );
document.write( "The total surface area of the small cubes is 64*6=384 cm sq.<BR>\n" );
document.write( "The increase in surface area is 384-96= 288 sq cm.<BR>\n" );
document.write( "The % increase in surface area is 288/96=300%<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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