You have 100 square feet of card board and want to build a box. The box is to have a square base and 4 sides but no top. What is the maximum volume that the box can contain?

a.Draw a sketch of the box. (You do not have to submit your sketch.)

Label the dimension of the 4 sides of the base b.

Label the dimension of the 4 sides of the height h.

b.What is the area of the base in terms of b?

c.What is the total area of the sides in terms of b and h?

d.The total area of the box A is 100 square feet. What is the equation which relates 100 to b and h? (i.e. A = f(b,h) = 100).

e.What is the total volume of the box V = f(b,h) in terms of b and h?

f.Using the equation you derived in (d), substitute for h in the volume equation so that you have V as a function only of b, i.e. V = f(b).

g.Plot your equation for V (= y) vs b (= x) in www.desmos.com/calculator

h.What is the maximum value for V from the plot? (Show a screen shot).

i.What is the value for b at the maximum value?Hint: b = 10/