A rectangular piece if sheet metal is twice as long as it is wide. Squares measuring 5 inches on a side are cut from each corner and the sides are folded...

Question

...(Continue of the question) to form a box. If the volume of the box is 1760 m^3, what are the dimensions of the sheet metal?

Solve and type an equation

Answer 1

Hi, Vivien.

 

Okay, so this is a little bit confusing unless you draw a rectangular model. The sheet metal dimensions are w x 2w  because the length is 2w inches and the width is w inches.

Now, if you draw a model of the sheet metal and draw the square in the corner which are 5 inches by 5 inches, then you will see that the dimensions of the box are :

length = 2w - 10

width = w - 10

height = 5

 

So now we can plug in our dimensions into the volume formula for the box:

l x w x h = 

(2w - 10)(w - 10)x5 = 1760

(2w - 10)(w - 10) = 352

2w² - 30w + 100 = 352

2w² - 30w -252 = 0

2(w²-15w -126) = 0

(w + 6)(w - 21) = 0

Since w can't be a negative number, 

w = 21 inches

 

So now we need the original dimensions of the sheet metal:

w = 21 inches

l = 2w = 42 inches

 

The only concern I have is that the squares cut out were in inches, but your volume measurement is in meters. You might want to double check and make sure the units are correct.