document.write( "Question 1189049: A rectangular parallelepiped is inscribed in a sphere whose diameter is 25 cm. find the volume of the parallelepiped if its length is 20 cm and its width is 12 cm. \n" ); document.write( "

Algebra.Com's Answer #820285 by ikleyn(52814) $\"\"$ $\"About$

You can put this solution on YOUR website!
.
\n" ); document.write( "A rectangular parallelepiped is inscribed in a sphere whose diameter is 25 cm.
\n" ); document.write( "find the volume of the parallelepiped if its length is 20 cm and its width is 12 cm.
\n" ); document.write( "~~~~~~~~~~~~~~~~~~~\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "

\r\n" );
document.write( "Notice that the longest 3D diagonal of the parallelepiped is the diameter of the sphere.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "So, apply the 3D Pythagorean formula\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "    25^2 = 20^2 + 12^2 + h^2 \r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "where h is the height of the parallelepiped, which is the only unknown its dimension.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "From the equation,  h =  =  = 9 cm.\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "Thus the volume of the parallelepiped is  20*12*9 = 2160 cubic centimeters.    ANSWER\r\n" );
document.write( "

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

\n" );