Question

An open box is to be constructed from a square piece of sheet metal by removing a square of side 5 feet from each corner and turning up the edges. If the box is to hold 720 cubic feet, what should be the dimensions of the sheet metal? What is the length of a side of the square piece of sheet metal? feet

Answer 1

a Solution : given that an open box is to be made from squale piece by cutting 5 feet from each corners. and Volume of box 720 cubic feet dimensions of the square piece of sheet metal. Let X be the length of a side of square Then According to Question figure will as follows E 45-4X-10)*65 To find be X ft > 1 x square sheet (X-10 Aftee cutting corners 5 feet 5 5 15 <(X-1o)» Hence ON folding cutting sheet in box height of box will be, h = 5 feet Length (x-10) feet width box will be, b=(x-10) feet box will be 2

Since we know that on putting we volume of box (base Area) at height = (length width ) height the values get. Volume of box = (x-10)*(x-10) 5 > 720 CX-10)? At 5 (x-10) 720 = 144 5 ². X-10 +12 X-10 is length, hence it cannot be Negative Flence X-10 =12 Х 10+12 X = 22 feet Hence The Length of a side of the square piece of sheet metal will be X = 22 feet 2

Hence the length of a side of square sheet will be, X = 22 feet