A box with an open top is to be constructed by cutting 1-inch squares from the corners of a rectangular sheet of tin whose length is twice its width. What size sheet will produce a box having a volume of 12in^3?

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Answer 1 · 2017-05-29T16:04:02

#(sqrt(6) + 2) " inches" xx (2sqrt(6) + 2) " inches"~~ 4.45 " in." xx 6.90 " in."#

Given: box length #= 2 * #width; #" "l = 2w#

The box size is #1# inch #xx w xx l#

Let the sheet size be #l + 2 " inches" xx w + 2 " inches"#

When you cut the #1# inch corners from the sheet, the size of the box length and width decreases by #2# inches.

#V_(b o x) = 1 xx w xx 2w = 12#

#2w^2 = 12#

#w^2 = 12/2 = 6#

#w = sqrt(6); " "# width of the box

#l = 2w = 2sqrt(6); " "# length of the box

Size of the sheet:

#(sqrt(6) + 2) " inches" xx 2sqrt(6) + 2 " inches" ~~ 4.45 " in." xx 6.90 " in."#

CHECK:

#V_(b o x) = 1 xx sqrt(6) xx 2sqrt(6) = 12 " in."^3#