SOLUTION: A box has a square bottom and top is 5 cm high. Find its volume if its total surface area is 192 cm².

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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.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let x= the side of the square bottom and top
The area of the bottom plus top is:
2x%5E2
The area of the 4 sides is:
4%2A5x+=+20x
Total surface area is:
2x%5E2+%2B+20x
given:
2x%5E2+%2B+20x+=+192
x%5E2+%2B+10x+=+96
I'll solve by completing the square:
x%5E2+%2B+10x+%2B+%2810%2F2%29%5E2+=+96+%2B+%2810%2F2%29%5E2
x%5E2+%2B+10x+%2B+25+=+96+%2B+25
Both sides are perfect squares
%28x+%2B+5%29%5E2+=+121
Take the square root of both sides
x+%2B+5+=+11
x+=+6
The box measures 6 cm x 6 cm x 5 cm
The volume is 6%2A6%2A5+=+180 cm3
check:
2%2A6%5E2+%2B+20%2A6+=+192
72+%2B+120=+192
192+=+192
OK