Posted by **Jen** on Saturday, November 18, 2006 at 10:16pm.

Applications of derivatives

You are planning to make an open rectangular box from an 8 by 15 inch piece of cardboard by cutting congruent squares from the corners and folding up the sides. what are the dimensions of the box of largest volume you can make this way, and what is its volume.

Let a be the height of the folded sides. The congruent squares that you cut away will have area of a^2 each. The volume of the box will be

V = (8-2a)(15 - 2a) a

= a (120 + 2a^2 -46 a)

Differentiate V with respect to a and set the derivative equal to zero, and solve for a.

u made a mistake..

instead of

= a (120 + 2a^2 -46 a)

it should be

= a (120 + 4a^2 -46 a)

The volume comes out to be 2450/27 in^3 and a = to 5/3

## Answer this Question

## Related Questions

- calculus - You are planning to make an open-top box from an 12 in by 12 in piece...
- Calculus - An open top box is made by cutting congruent squares from the corners...
- math - An open topped box can be created by cutting congruent squares from each ...
- math - An open box is made from a rectangular piece of cardboard, with ...
- math - An open-topped box is made from a rectangular piece of cardboard, with ...
- Math - An open-topped box can be created by cutting congruent squares from each ...
- math grade 12 - A open-topped box can be created by cutting congruent squares ...
- Math - A box with a rectangular base and no top is to be made from a 9 inch by ...
- math.....need help - Solve the problem. An open box is to be made from a ...
- Algebra - A box with no top is to be constructed from a piece of cardboard ...

More Related Questions