Question

you are planning to make an open rectangular box from a 10 by 18 cm piece of cardboard by cutting congruent squares from corners and folding up the sides. a) What are the dimensions of the box of largest volume you can make this way? b) What is its volume?....help thanks!

Answer 1

Need to find the volume first. Let x be lengths of sides of little squares you are cutting from the corners of the rectangle. They will form the height of your open box.
Folding these up will leave an area in the middle that is (18-2x)((10-2x) in dimension.
The volume will be V = x (18-2x)(1-2x). A max will occur when dV/dx =0.

If this is hard to find, some trial and error will get you close.

Answer 2

so the x values i got were 0,5, and 9.

Answer 3

@douglaswinslowcooper ^

Answer 4

and 5 is where the max occurs

Answer 5

You have solved V(x) = 0, but need to solve dV/dx = 0.
Could resort to trial and error with various x values to max V(x)= x(18-2x)(10-2x).

Answer 6

okay thanks i'll try that