document.write( "Question 538760: a box has a square bottom and top and is 5 cm high. can you find its volume if its total surface area is 192 cm squared? \n" ); document.write( "

Algebra.Com's Answer #353254 by KMST(5328) $\"\"$ $\"About$

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We want to know the length of the sides of that square bottom.
\n" ); document.write( "Let that length (in cm) be s.
\n" ); document.write( "The surface of the bottom (in square cm) is $\"s%5E2\"$ .
\n" ); document.write( "The surface of the top is the same.
\n" ); document.write( "The surface of the side walls (in square cm) equals the height in cm (5) times the perimeter of the bottom in cm (4s).
\n" ); document.write( "The total surface area is
\n" ); document.write( " $\"2%28s%5E2%29%2B5%284s%29=+2s%5E2%2B20s\"$
\n" ); document.write( "That gives us the equation
\n" ); document.write( " $\"2s%5E2%2B20s=192\"$ ---> $\"s%5E2%2B10s=96\"$ ---> $\"s%5E2%2B10s-96=0\"$
\n" ); document.write( "We solve that equation any way we can.
\n" ); document.write( "Factoring, $\"s%5E2%2B10s-96=%28s%2B16%29%28s-6%29\"$ , so the equation can be written as
\n" ); document.write( " $\"%28s%2B16%29%28s-6%29=0\"$ , which has the solutions $\"s=6\"$ and $\"s=-16\"$ .
\n" ); document.write( "Since the measurements of the box must be positive numbers, the only reasonable answer is $\"s=6\"$ .
\n" ); document.write( "The volume is $\"%286cm%29%286cm%29%285cm%29=180cm%5E3\"$ \n" ); document.write( "

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