document.write( "Question 1043186: A frustrum of pyramid consist of square base of length 10cm and a top square of 7cm the heights of the frustrum is 6cm calculate
\n" ); document.write( "(A) the surface area
\n" ); document.write( "(B)volume \n" ); document.write( "

Algebra.Com's Answer #658530 by ikleyn(52787) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A $\"highlight%28cross%28frustrum%29%29\"$ frustum of pyramid consists of square base of length 10 cm and a top square of 7 cm.
\n" ); document.write( "The heights of the $\"highlight%28cross%28frustrum%29%29\"$ frustum is 6 cm calculate
\n" ); document.write( "(A) the surface area
\n" ); document.write( "(B) volume
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "Volume\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "See this Wikipedia article or this WEB-page.\r\n" );
document.write( "\r\n" );
document.write( "The volume formula of a frustum of a square pyramid was introduced by the ancient Egyptian mathematics \r\n" );
document.write( "in what is called the Moscow Mathematical Papyrus, written ca. 1850 BC.:\r\n" );
document.write( "\r\n" );
document.write( "V =  \r\n" );
document.write( "\r\n" );
document.write( "where a and b are the base and top side lengths of the truncated pyramid, and h is the height. \r\n" );
document.write( "The Egyptians knew the correct formula for obtaining the volume of a truncated square pyramid, \r\n" );
document.write( "but no proof of this equation is given in the Moscow papyrus.\r\n" );
document.write( "

\r
\n" ); document.write( "\n" ); document.write( "By applying the formula, we get V = $\"%281%2F3%29%2A6%2A%2810%5E2+%2B+10%2A7+%2B+7%5E2%29\"$ = 438 $\"cm%5E3\"$ .\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "By the way, the proof is easy.\r\n" );
document.write( "As you know, the volume of the larger pyramid is   = , where  is its height.\r\n" );
document.write( "The volume of the smaller pyramid is   = , where  is its height.\r\n" );
document.write( "\r\n" );
document.write( "Obviously, from similarity  =   and   = , where const is a constant value independent of \"a\" and \"b\".\r\n" );
document.write( "\r\n" );
document.write( "Then   = ,   = .\r\n" );
document.write( "\r\n" );
document.write( "The volume of the frustum is the difference \r\n" );
document.write( "\r\n" );
document.write( "V =  =  =  = .\r\n" );
document.write( "\r\n" );
document.write( "But const*(a-b) =  = h, the height of the frustum.\r\n" );
document.write( "\r\n" );
document.write( "Therefore,  the volume of the frustum is  V = .   QED.\r\n" );
document.write( "

\n" ); document.write( " \n" ); document.write( "

\n" );