SOLUTION: 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?

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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?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
We want to know the length of the sides of that square bottom.
Let that length (in cm) be s.
The surface of the bottom (in square cm) is s%5E2.
The surface of the top is the same.
The surface of the side walls (in square cm) equals the height in cm (5) times the perimeter of the bottom in cm (4s).
The total surface area is
2%28s%5E2%29%2B5%284s%29=+2s%5E2%2B20s
That gives us the equation
2s%5E2%2B20s=192 ---> s%5E2%2B10s=96 ---> s%5E2%2B10s-96=0
We solve that equation any way we can.
Factoring, s%5E2%2B10s-96=%28s%2B16%29%28s-6%29, so the equation can be written as
%28s%2B16%29%28s-6%29=0, which has the solutions s=6 and s=-16.
Since the measurements of the box must be positive numbers, the only reasonable answer is s=6.
The volume is %286cm%29%286cm%29%285cm%29=180cm%5E3