Raymond has exactly 360 square inches of cardboard to make a box. He wants two of the dimensions to be 6 inches and the other one to be a whole number of inches. How many different size boxes can he make?
Width = 6 in.
Height = 6 in.
Length = L in.
As=2(W*h) + 2(L*h) + (2W*L) = 360in^2. = max. surface area.
2(6*6) + 2(L*6) + 2(6*L) = 360,
72 + 12L + 12L = 360,
24L = 360 - 72 = 288,
L = 12 in. = max length.
Lmin 1 in. = min whole number.
He can make 12 different sizes(L = 1 to
12in).