Posted by **Icy** on Sunday, June 17, 2007 at 5:02pm.

1. Chris makes an open-topped box from a 30-cm by 30-cm piece of cardboard by cutting out equal squares from the corners and folding up the flaps to make the sides. What are the dimensions of each square to the nearest hundredth of a centimetre, so that the volume of the resulting box is more than 100cm(cubic)?

2.A cylindrical vat must hold 5m(cubic) of liquid cake mix. The vat must be wider than it is tall, but no more than 3m in diameter. What dimensions will use the least amount of material?

The flap square is the height of the box.

Volume= (30-2h)^2 * h check that with a sketch.

max volume..

dV/dh= 2(30-2h)(-2h)+ (30-2h)^2=0

or 4h=30-2h or h=5

so check that to see if volume is greater than 100..

On the second, write the volume and surface area equations, then minimize surface area.

Thanks, I'll give it a try.

- Calculus -
**bob**, Wednesday, April 28, 2010 at 10:39am
cool^2

## Answer this Question

## Related Questions

- math - you want to make an open-topped box from a 20 cm by 20 cm piece of ...
- math - An open topped box can be created by cutting congruent squares from each ...
- math - Vanilla Box Company is going to make open-topped boxes out of 17 × 13-...
- Calculus - A box with an open top is to be made from a square piece of cardboard...
- calculus - You are planning to make an open-top box from an 12 in by 12 in piece...
- Calculus - A square sheet of cardboard with a side 16 inches is used to make an ...
- Math - Business Calc. - Chocolate Box Company is going to make open-topped ...
- Math - An open-topped box can be created by cutting congruent squares from each ...
- PRE-CALCULUS - AN OPEN BOX IS FORMED BY CUTTING SQUARES OUT OF A PIECE OF ...
- Calculus - A SHEET OF CARDBOARD 180 INCHES SQUARE IS USED to make an open box by...

More Related Questions