document.write( "Question 198085: A box has a square bottom and top is 5 cm high. Find its volume if its total surface area is 192 cm². \n" ); document.write( "

Algebra.Com's Answer #148552 by josmiceli(19441) $\"\"$ $\"About$

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Let $\"x\"$ = the side of the square bottom and top
\n" ); document.write( "The area of the bottom plus top is:
\n" ); document.write( " $\"2x%5E2\"$
\n" ); document.write( "The area of the 4 sides is:
\n" ); document.write( " $\"4%2A5x+=+20x\"$
\n" ); document.write( "Total surface area is:
\n" ); document.write( " $\"2x%5E2+%2B+20x\"$
\n" ); document.write( "given:
\n" ); document.write( " $\"2x%5E2+%2B+20x+=+192\"$
\n" ); document.write( " $\"x%5E2+%2B+10x+=+96\"$
\n" ); document.write( "I'll solve by completing the square:
\n" ); document.write( " $\"x%5E2+%2B+10x+%2B+%2810%2F2%29%5E2+=+96+%2B+%2810%2F2%29%5E2\"$
\n" ); document.write( " $\"x%5E2+%2B+10x+%2B+25+=+96+%2B+25\"$
\n" ); document.write( "Both sides are perfect squares
\n" ); document.write( " $\"%28x+%2B+5%29%5E2+=+121\"$
\n" ); document.write( "Take the square root of both sides
\n" ); document.write( " $\"x+%2B+5+=+11\"$
\n" ); document.write( " $\"x+=+6\"$
\n" ); document.write( "The box measures 6 cm x 6 cm x 5 cm
\n" ); document.write( "The volume is $\"6%2A6%2A5+=+180\"$ cm3
\n" ); document.write( "check:
\n" ); document.write( " $\"2%2A6%5E2+%2B+20%2A6+=+192\"$
\n" ); document.write( " $\"72+%2B+120=+192\"$
\n" ); document.write( " $\"192+=+192\"$
\n" ); document.write( "OK \n" ); document.write( "

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