Question

An open box is to be made from a square piece of cardboard of perimeter 20 cardboard by cutting four equal square pieces from each corner and turning up the sides. What is the ide length of the pieces that should be cut out so that the box will have maximum volume?
A. 10"
B. 10/3 "
C. 3 "
D. 5 "

Answer 1

20/4 = 5 each side of your material is gonna be 5 wide; we need to remove an x by x piece from the sides so volume of the box is:

Vb = x * (5-x-x) * (5-x-x) = x(5-2x)^2 = 4x^3 -20x^2 +25x

To find the max volume we derive this to get:

Vb' = 12x^2 -40x +25

Vb' = 0 = max

Answer 2

we can narrow the choice to B or C simply because they are improbable

Answer 3

plug in those values to Vb and see what you get :)

3(4(9) -20(3) + 25)

3(36 - 60 + 25)

3(1) = 3

Answer 4

(10/3) (4(100/9) -20(10/3)+25) = 9.26

id go with b