# 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?

May 29, 2017

$\left(\sqrt{6} + 2\right) \text{ inches" xx (2sqrt(6) + 2) " inches"~~ 4.45 " in." xx 6.90 " in.}$

#### Explanation:

Given: box length $= 2 \cdot$width; $\text{ } l = 2 w$

The box size is $1$ inch $\times w \times l$

Let the sheet size be $l + 2 \text{ inches" xx w + 2 " inches}$

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

${V}_{b o x} = 1 \times w \times 2 w = 12$

$2 {w}^{2} = 12$

${w}^{2} = \frac{12}{2} = 6$

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

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

Size of the sheet:

$\left(\sqrt{6} + 2\right) \text{ inches" xx 2sqrt(6) + 2 " inches" ~~ 4.45 " in." xx 6.90 " in.}$

CHECK:

${V}_{b o x} = 1 \times \sqrt{6} \times 2 \sqrt{6} = 12 {\text{ in.}}^{3}$