Question

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?

Answer 1

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

Explanation:

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`