An open box is to be constructed from a rectangular sheet of tin 3 meters wide by cutting out a 1-meter square from each corner and folding up the sides. The volume of the box is to be 2 cubic meters. What is the length of the tin rectangle?

Answer 1

V = area of base * height

Since 1m was cut from each corner, the base is just 1m wide now. Likewise, since the cut was 1m deep, the height is now 1m.

So, the volume = width * height * length
2 = 1 * 1 * length

what, oh, what could be the length?
2? NO! That's the length of the box. The tin sheet has to be 4m long, so the 1m corners can be cut out.

Answer 2

Draw a picture showing width = 3 and
Draw the corner cutouts.
Label the length of each edge
If the total length of the sheet is X,
Then, (X - 2)(1)(1) = 2 making X = 4 meters.

Answer 3

V = area of base * height

Since 1m was cut from each corner, the base is just 1m wide now. Likewise, since the cut was 1m deep, the height is now 1m.

So, the volume = width * height * length
2 = 1 * 1 * length

what, oh, what could be the length?
2? NO! That's the length of the box. The tin sheet has to be 4m long, so the 1m corners can be cut out.
Algebra - tchrwill, Tuesday, October 4, 2011 at 10:40am

Draw a picture showing width = 3 and
Draw the corner cutouts.
Label the length of each edge
If the total length of the sheet is X,
Then, (X - 2)(1)(1) = 2 making X = 4 meters.