Problema Solution
You have to make a square-bottomed, no lid box with a height of three inches and a volume of approximately 42 cubic inches. You will be taking a piece of cardboard, cutting three-inch squares from each corner, scoring between the corners, and folding up the edges. What should be the dimensions of the cardboard, to the nearest quarter inch ?
Answer provided by our tutors
let
h = 3 in the height of the box
b = side of the squared bottom of the box
V = 42 in^3 the volume of the box
V = b*b*h the volume of the square-bottomed box
b*b*3 = 42
b*b = 42/3
b*b = 14
b = √14
the dimensions of the cardboard are
w = b + 2h = 2√14 + 2*3 = 6 + 2√14 =9.74in = 9 3/4 in
l = b + 2h = 2√14 + 2*3 = 6 + 2√14 = 9 3/4 in
the dimensions of the cardboard should be 9 3/4 in to the nearest quarter inch.