On a rectangular piece of cardboard with perimeter 11 inches, three parallel and equally spaced creases are made
On a rectangular piece of cardboard with perimeter 11 inches, three parallel and equally spaced creases are made (see Figure 1). The cardboard is then folded along the creases to make a rectangular box with open ends (see Figure 2). Letting x represent the distance (in inches) between the creases, use the graphing calculator to find the value of x that maximizes the volume enclosed by this box. Then give the maximum volume. Round your responses to two decimal places....
A Candy box is made from a piece of cardboard that meaasures 11 by 7 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box. What size square should be cut from each corner to obtain maximum volume?
A box with a lid is to be made from a rectangular piece of cardboard measuring 24 cm by 72 cm. Two equal squares of side x are to be removed from one end, and two equal rectangles are to be removed from the other end so that the tabs can be folded to form a box with a lid. Find x such that the volume of the box is a maximum. Lid 24 cm 72 cm Type an integer...
8. (10pts) A rectangular filed is to be enclosed with a fence. One side of the field is against an existing wall, so that no fence is needed on that side. If material for the fence costs $2 per foot for the two ends and $4 per foot for the side parallel to the existing wall, find the dimensions of the field of largest area that can be enclosed for $1000, 9. (11pts) A candy box is made from a...
You construct an open box from a square piece of cardboard, 24 inches on a side, by cutting out equal squares with sides of length from the corners and turning up the sides (see figure below). Write a function V, in terms of 2, that represents the volume of the box. Then use a calculator to graph V and use the graph to estimate the value of that produces a maximum volume. - - - - x - - x...
To create an open-top box out of a sheet of cardboard that is 6 inches long and 5 inches wide, you make a square flap of side length x inches in each corner by cutting along one of the flap's sides and folding along the other. Once you fold up the four sides of the box, you glue each flap to the side it overlaps. To the nearest tenth, find the value of x that maximizes the volume of the...
You are planning to make an open rectangular box from a 40-in.-by-79-in. piece of cardboard by cutting congruent squares from the comers and folding up the sides. What are the dimensions of the box of largest volume you can make this way, and what is its volume? arate answers as needed) The dimensions of box of maximum volume are (Round to the nearest hundredth as needed. Use a The maximum volume is 01 (Round to the nearest hundredth as needed.)...
A candy box is made from a piece of cardboard that measures 25 by 14 inches. Squares of equal size will be cut out of each corner. The sides will then be folded up to form a rectangular box. Find the length of the side of the square that must be cut out if the volume of the box is to be maximized. What is the maximum volume? 14 in. A square with a side of length of 2.88 inches...
4. A rancher with 300 ft of fence intends to enclose a rectangular corral, dividing it in half by a fence 5. A rectangular garden of area 75 ft2 is bounded on three sides by a wall costing $8 per ft and on the 6. An open box is made from a 16 x 16 cm piece of cardboard by cutting equal squares from each corner parallel to the short sides of the corral. How much area can be enclosed?...
An open box is made from a square piece of cardboard 20 inches on a side by cutting identical squares from the corners and turning up the sides.(a) Express the volume of the box, V , as a function of the length of the side of the square cut from each corner, x. (b) Find and interpret V (1),V (2),V (3),V (4), and V (5). What is happening to the volume of the box as the length of the side...