An open box is to be made from a rectangular piece of cardboard which is 12 inches by 20 inches by cutting equal squares from the corners and turning up the sides. find the size of the square which gives the box of largest volume.

side of the square    x  =  2.43 in

Area of the square   x² =  5.91 in²

Step-by-step explanation:

The piece of cardboard  is

20  in    *      12    in    (rectangle)   we are going to cut four squares each in a corner of that piece then

V(b)  =  ( 12  - 2x )* ( 20 - 2x) *x

V(b)  =  ( 240 - 24x - 40x + 4x² ) *x          V(b)  = ( 240 -  64x  + 4x²)*x

V(b)  = 240x  - 64x²  +  4x³

Taking derivatives both sides of equation

V´(b)  =  240  - 128x  + 12x²

Then    V´(b)  =  0          240  - 128x  + 12x²  = 0

A second degree equation solving we have

12x²  -128x  + 240  = 0     ⇒  3x² - 32x  + 60

x₁,₂  = [ 32 ± √(32)² - 720] / 6    ⇒  x₁,₂  = [ 32 ± 17.44]/6

x₁  =  8.24 in   we dismiss this value since 2 times this value is bigger than one side which is not possible

x₂  =  2.43 in  then the square is  (2.43)² =  5.91 in²

your answer is 228

step-by-step explanation:

add the top and bottom bases together, then divide them by 2, then multiply by the height.

imma say 16%. sorry if its wrong. i'm doing the same stuff right now

step-by-step explanation: