# Math

posted by .

A Candy box is made from a piece of cardboard that meaasures 11 by 7 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box. What size square should be cut from each corner to obtain maximum volume?

• Math -

Let squares of size x" be cut from the corners.

Volume of (open) box
=V(x)
=height*length*width
=x(11-2x)(7-2x)
=4x^3-36x^2+77x

For maximum (or minimum), equate derivative to zero:
dV(x)/dx = 12x²-72x+77=0
Solve for x to get
x=3±(√93)/6
=1.39 or 4.61 (approximately)

4.61 is clearly not a feasible solution (because 2*4.61 > 7") and will be rejected.

So the cut-outs will be squares of 1.39" (approximately).

Now verify that the solution so obtained is a maximum by ensuring that d²V(x)/dx² < 0:
d²V(x)/dx² = 24x-72 = -38.6 <0 OK.

## Similar Questions

1. ### Calculus

A box with an open top is to be made from a square piece of cardboard by cutting equal squares from the corners and turning up the sides. If the piece of cardboard measures 12 cm on the side, find the size of the squares that must …
2. ### Calculus

Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 3 ft by 4 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that …
3. ### maths

an open box of rectangular base is to be made from 24 cm by 45cm cardboard by cutting out squares sheets of equal size from each corner and bending the sides.find the dimensions of the corner squares to obtain a box having largest …
4. ### Math

Arlan needs to create a box from a piece of cardboard. The dimensions of his cardboard are 10 inches by 8 inches. He must cut a square from each corner of the cardboard, in order to form a box. What size square should he cut from each …
5. ### math 12

\$identical\:squares\:are\:cut\:from\:each\:corner\:of\:a\:rectangular\:piece\:of\:cardboard,\:7\:cm\:by\:10\:cm.\:The\:sides\:are\:then\:folded\:up\:to\:make\:a\:box\:with\:an\:open\:top.\:If\:the\:volume\:of\:the\:box\:is\:25\:cubic\:centimeter,\:how\:long\:is\:the\:side\:of\:each\:square?
6. ### math

The length of a rectangular piece of cardboard is three more than twice the width. A square 2 cm on a side is cut out of each corner. The sides are folded up to form an open box. if the volume of the box is 120cm^3, what were the original …
7. ### Math

a rectangular piece of cardboard is twice as long as it is wide . from each of its for corners, a square piece 3 inches on a side cut out. the flaps at each corner are then turned up to form an open box. if the volume of the box is …
8. ### Calculus

Squares with sides of length x are cut out of each corner of a rectangular piece of cardboard measuring 3 ft by 4 ft. The resulting piece of cardboard is then folded into a box without a lid. Find the volume of the largest box that …
9. ### Pre-calculus

A square of size x inches is cut out of each corner of an 8in by 12in piece of cardboard, and the sides are folded up to form an open-topped box. Determine the dimensions of the cut-out squares that will produce the box of maximum …
10. ### precalculus

A square of size x inches is cut out of each corner of an 8in by 12in piece of cardboard, and the sides are folded up to form an open-topped box. Determine the dimensions of the cut-out squares that will produce the box of maximum …

More Similar Questions