Posted by **irma** on Sunday, May 12, 2013 at 1:38am.

a square sheet of tin 30cm on a side is to be used to make an open - top box by cutting a small square of tin from each corner and bending up the sides. how large should be the square cut from each corner to make the box's volume as large as possible

- math -
**Reiny**, Sunday, May 12, 2013 at 6:43am
let the size of the cut-out square be x cm by x cm

then after bending,

the base of the box will be 30-2x by 30-2x and x cm high

Volume = x(30-2x)^2

= x(900 - 120x + 4x^2)

= 4x^3 - 120x^2 + 900x

d(Volume)/dx = 12x^2 - 240x + 900

= 0 for a max/min of Volume

12x^2 - 240x + 900 = 0

x^2 - 20x + 75 = 0

(x-5)(x-15) = 0

x = 5 or x = 15 , (clearly x = 15 yields a minimum volume of 0)

So the size of the cut should be squares of 5 cm by 5 cm.

## Answer This Question

## Related Questions

- algebra - An open box is to be constructed from a rectangular sheet of tin 5 ...
- Calculus - an open top box is to be made by cutting congruent squares of side ...
- Algebra - An open box is to be constructed from a rectangular sheet of tin 3 ...
- inermediate algebra - A box with no top is to be made by cutting a 2-inch square...
- Calculus (Optimization) - A rectangular piece of cardboard, 8 inches by 14 ...
- math,algebra - an open box is to be made by cutting small congruent squares ...
- math - application of derivatives: an open box is to be made by cutting small ...
- caculas - an open box is to be made by cutting small congruent squares from ...
- math - it is required to make an open box of gregreatest possible volume from a ...
- maths - a square piece of tin 31cm and20cm is to be made into a box without top,...

More Related Questions