document.write( "Question 701028: Either a right cylinder or a cube can be formed by bending the same rectangular sheet of aluminum. Neither the cylinder nor the cube will have a bottom or top. Find the volume of the cylinder if the volume of the cube is 27pi/4 cm3. Plaese show me step by step .Thanks \n" ); document.write( "
Algebra.Com's Answer #432209 by ankor@dixie-net.com(22740)\"\" \"About 
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Either a right cylinder or a cube can be formed by bending the same rectangular sheet of aluminum.
\n" ); document.write( " Neither the cylinder nor the cube will have a bottom or top.
\n" ); document.write( " Find the volume of the cylinder if the volume of the cube is 27pi/4 cm3.
\n" ); document.write( ":
\n" ); document.write( "let x = one side of the cube
\n" ); document.write( "then the sheet of aluminum will be 4x by x
\n" ); document.write( "and the volume of cube:
\n" ); document.write( "x^3 = \"%2827pi%29%2F4\"
\n" ); document.write( ":
\n" ); document.write( "The cylinder,
\n" ); document.write( "4x = the circumference of the cylinder
\n" ); document.write( " and
\n" ); document.write( "x = the height
\n" ); document.write( "Use the circumference to find the radius of the cylinder
\n" ); document.write( "\"2pi%2Ar+=+4x\"
\n" ); document.write( "\"pi%2Ar+=+2x\"
\n" ); document.write( "\"r+=+%282x%29%2Fpi\"
\n" ); document.write( "Find the volume of cylinder: \"A+=+pi%2Ar%5E2%2Ah\", replacing r and h
\n" ); document.write( "V = \"pi%2A%28%282x%29%2Fpi%29%5E2%2Ax\"
\n" ); document.write( "V = \"pi%2A%28%284x%5E2%29%2Fpi%5E2%29%2Ax\"
\n" ); document.write( "cancel pi
\n" ); document.write( "V = \"%28%284x%5E3%29%2Fpi%29\"
\n" ); document.write( "We know from the vol of the cube that x^3 = \"%2827pi%29%2F4\"
\n" ); document.write( "V = \"%28%284%2827pi%29%2F4%29%2Fpi%29\"
\n" ); document.write( "Cancel the 4
\n" ); document.write( "V = \"%28%2827pi%29%29%2Fpi\"
\n" ); document.write( "Cancel pi
\n" ); document.write( "V = 27 cu/cm is the volume of the cylinder
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\n" ); document.write( "Hey student, did this actually make sense? It's the end of the day for me and I am not thinking very well. Hope it does. C
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