16 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 square with a side

Q: Find the length and width of a rectangle with a perimeter 160 and whose area is a maximum.

A:

Q: Of all rectangles with a perimeter of 32, which one has the maximum area? (Give the dimensions.) The…

A: Here we have to find the length and width of the rectangle that has perimeter of 32 with maximum…

Q: A 39-inch by 104-inch piece of cardboard is used to make an open-top container by removing a square…

A:

Q: Find the length and width of a rectangle taht has an area 968 square feet and whose perimeter is a…

A: Let x and y(in feet) be the length and width of the rectangle Then area of rectangle is

Q: You are to fence off two rectangular garden beds of the same size in such a way that they share one…

A:

Q: An open-top bin is to be made from a 32-inch by 42-inch piece of plastic by removing a square from…

A: We have given a rectangular piece,

Q: According to postal regulations, a carton is classified as “oversized” if the sum of its height and…

A: Assume a be the side length of the square base,h be the height of the carton and V be the volume of…

Q: Of all rectangles with a fixed perimeter of P, which one has the maximum area? (Give the dimensions…

A:

Q: Of all rectangles with a fixed perimeter of P, which one has the maximum area? (Give the dimensions…

A: Let the length of a rectangle is x  Let the width of the rectangle be y

Q: A farmer wants to fence a rectangular field and then divide it in half with a fence down the middle…

A:

Q: A candy box is made from a piece of cardboard that measures 45 by 24 inches. Squa

A: Given: A candy box is made from a piece of cardboard that measures  45 by 24 inches. Squares of…

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area. Perimeter:…

A:

Q: An open-top box is to be made from a 12-inch by 30-inch piece of plastic by removing a square from…

A: This is  a problem related to maxima and minima. Based on the genera formula and concept we will…

Q: An open box is to be made from a square piece of material, 12 inches, by cutting equal squares from…

A: Here we use the concept of APPLICATIONS OF DERIVATIVES

Q: A 27-inch by 72-inch piece of cardboard is used to make an open-top box by removing a square from…

A: Let assume that side of square which should be cut out from each corner = xSo dimensions of open top…

Q: A company ships notepads in rectangular boxes that each have inside dimensions measuring 9 inches…

A: Consider the given information.

Q: An open box will be made by cutting a square from each corner of a 10-cm by 16-cm piece of cardboard…

A: To find: The size of square to be cut from the corner of cardboard to maximize volume and also find…

Q: Of all rectangles with a perimeter of 28​,which one has the maximum​ area? (Give the​ dimensions.)

A: We can find the dimensions as below.

Q: Find the dimensions of the rectangular box of maximum volume if the sum of the length, width, and…

A: To find dimension of the rectangular box of maximum volume  Given sum of length, width and height…

Q: An open box is made from an 8 inch x 8 inch piece of cardboard by cutting equal squares from each…

A: Volume of the box

Q: An open box (no top) is to be made by cutting congruent squares from each corner of a 12-inch by…

A:

Q: A shipping company must design a closed rectangular shipping crate with a square base. The volume is…

A: Given  Volume of the box = 36814 ft3  Cost of the material for top and sides are = $3 per square…

Q: An airline policy states that all baggage must be box-shaped with a sum of the length, width, and…

A: Given data is: The sum of the length, width, and height not exceeding 120 inches. To find the…

Q: A rancher plans to make four identical and adjacent rectan- gular pens against a barn, each with an…

A: Let the width of each pen be x and the length of each pen be y. As the pens are rectangular thus the…

Q: What is the maximum volume of an open box that can be made from a square piece of cardboard, 10in on…

A:

Q: A 39-inch by 104-inch piece of cardboard is used to make an open-top conatiner by removing a square…

A: Volume: A 39-inch by 104-inch piece of cardboard is used to make an open-top conatiner by removing a…

Q: A farmer plans to make 3 identical and adjacent rectangular pens, using an existing wall as one…

A:

Q: A man wants to construct a rectangular enclosure around his model railroad. Only three sides must be…

A: Ans. Let the length of enclosure is x &             width of enclosure is y

Q: An open top box is to be formed by cutting squares of equal sides from 15m by 15m square peice of…

A: Let the length of small square = x Hence, length of the big square = 15 - x - x = 15 - 2x Therefore,…

Q: A rectangular box without a lid is to be made from 12m2 of cardboard. Find the maximum volume of…

A:

Q: A rectangular plot of farmland will be bounded on one side by a river and on the other three sides…

A:

Q: A 22-inch by 70-inch piece of cardboard is used to make an open-top box by removing a square from…

A: Given:size of cardboard= 22in by 70 in

Q: A rectangular lot having an area of 5000 sq. meters is to be fenced on three sides. Find the minimum…

A: Both these questions can be solved by applying the concept of maxima and minima.

Q: A 27-inch by 72-inch piece of cardboard is used to make an open-top box by removing a square from…

A: Let x be side of the square which is cut in each corner then find volume of box.  Then solve for x.

Q: Find the dimensions of a rectangle of area 255 square centimeters that has the least perimeter.…

A: Given  The a rectangle of area 255 square centimetres .

Q: A 24-centimeter by 119-centimeter piece of cardboard is used to make an open-top box by removing a…

A: The 24-cm by 119-cm piece of cardboard used to make an open top box by removing from each corner of…

Q: What is the maximum area that can be completed with 240 feet of fencing? What are the dimensions?

A:

Q: When enclosing 3 sides, the maximum area for a given rectangular area is obtained by forming a…

A: Given:Length is twice the ?

Q: Find the length and width of a rectangle that has the given perimeter and a maximum area Perimeter:…

A:

Q: A rectangular box without a lid is to be made from 12 m2 of cardboard. Find the maximum volume of…

A: Given that a rectangular box without a lid is to be made from 12 m² of cardboard.

Q: square corners are cut out so that the sides can be folded up to make a box. What dimensions will…

A:

Q: A grain silo has the shape of a right circular cylinder topped by a cone. The approximate area of…

A: Given- The approximate area of the circular base is 452.39 ft2, the total height of cylinder and…

Q: A farmer has 1,200 feet of fence and wishes to build two identical rectangular enclosures, as in the…

A:

Q: You are to fence off two rectangular garden beds of the same size in such a way that they share one…

A:

Q: framer has 160 feet of fencing to enclose two adjacent rectangular pens. what dimensions should he…

A:

Q: A farmer has 1,300 feet of fence and wishes to build two identical rectangular enclosures, as in the…

A: Given: A farmer has 1,300 feet of fence and wishes to build two identical rectangular enclosures as…

Q: A carpenter is building a rectangular room with a fixed perimeter of 116 ft. What dimensions would…

A:

Q: Some airlines have restrictions on the size of items of luggage that passengers are allowed to take…

A: The given problem is solved below in detail.

Q: rectangular closed box with a square base is to have a capacity of 27 cubic meter. Determine the…

A: Given: A rectangular closed box with a square base is to have a capacity of 27 cubic meter. To find:…