document.write( "Question 868327: A rectangular pyramid has a volume of 190 cubic centimeters. Find two possible sets of measurement for the base area and height of the pyramid \n" ); document.write( "
Algebra.Com's Answer #523476 by jim_thompson5910(35256)![]() ![]() ![]() You can put this solution on YOUR website! The volume of a pyramid is\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "V = (1/3)*A*h\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "where V is the volume, A is the area of the base, h is the height.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Plug in V = 190 and isolate A*h to get\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "V = (1/3)*A*h\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "190 = (1/3)*A*h\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "190*3 = A*h\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "570 = A*h\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Now solve for either A or h. I'm going to solve for A to get\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "570 = A*h\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "570/h = A\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A = 570/h\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Now we can plug in arbitrary values of h to get corresponding values of A.\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "For example, if h = 1, then\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A = 570/h\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A = 570/1\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A = 570\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "Or if h = 2, then\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A = 570/h\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A = 570/2\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A = 285\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "So two possible sets of measurement for the base area A and the height h are: \r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "A = 570, h = 1 \n" ); document.write( "A = 285, h = 2\r \n" ); document.write( " \n" ); document.write( " \n" ); document.write( "\n" ); document.write( "There are infinitely more combos (just make sure both A and h are positive). \n" ); document.write( " |