Posted by **Jacob** on Friday, March 8, 2013 at 4:55pm.

If an open box is made from a tin sheet 7 in. square by cutting out identical squares from each corner and bending up the resulting flaps, determine the dimensions of the largest box that can be made. (Round your answers to two decimal places.)

Height:

Length:

Width:

- Applied Calculus -
**Reiny**, Friday, March 8, 2013 at 6:25pm
base = 7- 2x

height = x

volume = x(7-2x)^2

= 49x - 28x^2 + 4x^3

d(volume)/dx = 49 - 56x + 12x^2

= 0 for a max volume

12x^2 - 56x + 49 = 0

x = (56 ± √784)/24

= (56 ± 28)/24 = 3.5 or 7/6 or 1.1666...

but clearly x < 3.5 or we have cut the whole base away.

base is 7 - 2(7/6) = 14/3 by 14/3

and the height is 7/6

round to your required decimals

- Applied Calculus -
**Damon**, Friday, March 8, 2013 at 6:28pm
new length = 7 - 2 h

height = h

volume = (7-2h)(7-2h)(h)

v = (49 -28 h + 4 h^2)h

so

v = 4 h^3 -28 h^2 + 49 h

dv/dh = 0 for max or min

dv/dh = 12 h^2 -56 h + 49 = 0

(6h -7)(2 h -7) = 0

h = 7/6 or h = 7/2

if h = 7/2, the box has zero bottom

so the answer is h = 7/6

7 - 2(7/6) = 7-7/3 = 14/3 = length and width

## Answer This Question

## Related Questions

- Calculus - By cutting away identical squares from each corner of a rectangular ...
- maths - an open box of rectangular base is to be made from 24 cm by 45cm ...
- Calculus - an open top box is to be made by cutting congruent squares of side ...
- calculus - An open box is to be made out of a 8-inch by 14-inch piece of ...
- calculus - By cutting away identical squares from each corner of a rectangular ...
- calculus optimization problem - by cutting away identical squares from each ...
- math - By cutting away identical squares from each corner of a rectangular ...
- calculus - An open box is to be made out of a 10-inch by 14-inch piece of ...
- Calc - An open box is to be made out of a 10-inch by 16-inch piece of cardboard ...
- math - a square sheet of tin 30cm on a side is to be used to make an open - top ...

More Related Questions