A cardboard box without a lid is to have a volume of 10,976 cm3. Find the dimensions that minimize the amount of cardboard used. (Let x, y, and z be the dimensions of the cardboard box.)

28cm*28cm*14cm

Step-by-step explanation:

Five side box for cardboard are: xy, 2xz and 2yz

so the function of Area will be:

  equation 1

The Volume will be:

       equation 2

we can make z the subject of the formula by divide both side by xy

now   z =       equation 3

To eliminate z, substitute z into equation 1

f(x,y)=xy+2x+2y

f(x,y)=xy++

Now we have to derivative of x and y

for y and x

substitute y into x

to find y

to find z

z=

so The dimensions are 28cm*28cm*14cm

6 spoons of sugar for every 21 cups of flour

step-by-step explanation: