SOLUTION: A 2" square is cut from each corner of a rectangler piece of sheet metal. The metal is bent up to form a box with no top. The length of the box is 5" more than the width. The volum

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A 2" square is cut from each corner of a rectangler piece of sheet metal. The metal is bent up to form a box with no top. The length of the box is 5" more than the width. The volum      Log On


   

Question 183609: A 2" square is cut from each corner of a rectangler piece of sheet metal. The metal is bent up to form a box with no top. The length of the box is 5" more than the width. The volume of the box is 168 in^3.
Find: the surface area of the box?
note: Define var. define other quantities as needed, write a quadratic equation in one var., solve.
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let w in = the width of the box
Let V in3 = volume of the box
given:
length = w+%2B+5 in
height = 2 in
V+=+168 in3
------------------------
V+=+w%2A%28w+%2B+5%29%2A2
V+=+2%2A%28w%5E2+%2B+5w%29
V+=+2w%5E2+%2B+10w
168+=+2w%5E2+%2B+10w
2w%5E2+%2B+10w+-+168+=+0
w%5E2+%2B+5w+-+84+=+0
Solve using quadratic formula
w+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
a+=+1
b+=+5
c+=+-84
w+=+%28-5+%2B-+sqrt%28+5%5E2-4%2A1%2A%28-84%29+%29%29%2F%282%2A1%29+
w+=+%28-5+%2B-+sqrt%28+25+%2B+336+%29%29%2F2+
w+=+%28-5+%2B-+sqrt%28+361+%29%29%2F2+
w+=+%28-5+%2B-+19%29%2F2+
w+=+-12 Can't use a negative value here
w+=+7
and
w+%2B+5+=+12
If I flatten out the box and put the 4 square cut-outs from
the corners back, then 4 inches gets added to the width
and 4 inches to the length.
w+%2B+4 is the width of flattened box
w+%2B+5+%2B+4 is the length of the flattened box
Area = %287+%2B+4%29%2A%287+%2B+5+%2B+4%29
Area = 11%2A16
Area = 176 in2