SOLUTION: A box has a square top and bottom. The height of the box is 5cm. Find its volume if the total surface area is 192cm^2

Algebra ->  Surface-area -> SOLUTION: A box has a square top and bottom. The height of the box is 5cm. Find its volume if the total surface area is 192cm^2      Log On


   

Question 636313: A box has a square top and bottom. The height of the box is 5cm. Find its volume if the total surface area is 192cm^2
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Volume+=+length%2Awidth%2Aheight...where, in your case, length=width
so, Volume+=+length%5E2%2A5cm
Surface_+area=SA%29+...= >...surface areas of all the sides
Two sides have square areas and the other four sides have rectangular areas:
SA+=+x%5E2+%2B+x%5E2+%2B+5x+%2B+5x+%2B+5x+%2B+5x+
SA+=+2x%5E2+%2B+20x+
given: SA=192
192=2x%5E2+%2B20x+
or
2x%5E2+%2B20x=192
2x%5E2+%2B20x-192=0......divide by 2 and solve for x
x%5E2+%2B10x+-+96+=+0
%28x+%2B+16%29%28x+-+6%29+=+0
x+=+6+cm or x=-16cm
Pick only x+=+6+cm, since length is positive.
Now use x+=+6cm in the volume equation
V+=+%286cm%29%5E2%2A5cm+=+36cm%5E2%2A5cm=180cm%5E3