# Calculus

posted by .

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 -

cool^2

## Respond to this Question

 First Name School Subject Your Answer

## Similar Questions

1. ### math

you want to make an open-topped box from a 20 cm by 20 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 …
2. ### calculus

You are planning to make an open-top box from an 12 in by 12 in piece of cardboard by cutting congruent squares from the corners and folding up the sides. What are the dimensions (of the 3 sides) of the largest volume you can make …
3. ### math

An open-topped box is made from a rectangular piece of cardboard, with dimensions of 24 cm by 30 cm, by cutting congruent squares from each corner and folding up the sides. Determine the dimensions of the squares to be cut to create …
4. ### 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 …
5. ### math

An open topped box can be created by cutting congruent squares from each of the 4 corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. Determine the dimensions of the squares that must be cut …
6. ### math grade 12

A open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. Derermine the dimensions of the square that must be cut …
7. ### Math

An open-topped box can be created by cutting congruent squares from each of the four corners of a piece of cardboard that has dimensions of 20cm by 30cm and folding up the sides. Determine the dimensions of the squares that must be …
8. ### Calculus

A square sheet of cardboard with a side 16 inches is used to make an open box by cutting squares of equal size from the four corners and folding up the sides. What size squares should be cut from the corners to obtain a box with largest …
9. ### Calculus

An open box is formed from a piece of cardboard 12 inches square by cutting equal squares out of the corners and turning up the sides, find the dimensions of the largest box that can be made in this way.
10. ### calculus

Chocolate Box Company is going to make open-topped boxes out of 7 × 11-inch rectangles of cardboard by cutting squares out of the corners and folding up the sides. What is the largest volume box it can make this way?

More Similar Questions