Question

An open box is to be made from a rectangular piece of cardboard, 7 inches by 3 inches by cutting equal squares from each corner and turning the sides up. Find the maximum volume for the box and the dimensions of the square that should be cut from each corner to achieve that volume

Answer 1

so draw a picture to help, for somereason i cant draw on here
draw a rectangle with side lengths 7 and 3, at each corner draw squares that would be the bits cut out. call the length and width of each square "a"

the length of your folded up thing will be 7-2a, the width, 3-2a, the height will be a

V = length times width times height = (7-2a)(3-2b)a
= 4a^3 -20a^2 +12a

this is at a maximum when dV/da = 0

when

12a^2 -40a +21 = 0

solve for a

plug that back in to the equation for V to get maximum volume

Answer 2

Thanks

Answer 3

I dont understand what you did after dv/da

Answer 4

i took the derivative of V with respect to a

Answer 5

so how i solve for a?

Answer 6

wouldnt it be +12 instead of +21?

Answer 7

your absolutely right, thats a typo

Answer 8

solve for a using quadratic equation

Answer 9

also when you foil its -2a not -2b. i appreciate help but please make sure its typed right it can really confuse a person.