An open box is to be made from a 3 ft by 8 ft rectangular piece of sheet metal by cutting out squares of equal size from the four corners and bending up the sides. Find the maximum volume that the box can have. Round your answer to the nearest integer. The maximum volume is i ft3.

Q: Suppose that 208 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Given:  208 ft of fencing is used to enclose a coral From given figure diameter of the semicircle is…

Q: The sum of its length and girth (the distance around) does not exceed 96 in.  What dimensions will…

A:

Q: A standard elevator in a midrise building can hold a maximum weight of about 3 2/3 tons. Assuming an…

A: We first convert tons into pounds

Q: An expecting mother wants to convert a corner of the nursery in her house into a rectangular playpen…

A: Let x and y be the dimension of the rectangular playpen. Given

Q: An open-top box with a square base is to have a volume of 32 cubic feet. Find the dimensions of the…

A: To determine the dimension of the box which minimize the amount of material used.

Q: What is the maximum area of a rectangle that can be inscribed in a right triangle with a base 8 cm…

A: This question can be solved using the concept of maxima and minima.

Q: What is the maximum area of a rectangle that can be inscribed in a right triangle with a base 8 cm…

A:

Q: A rectangle has a perimeter of 112 ft then the dimensions of the rectangle with maximum area is a)…

A:

Q: A cylinder with a radius of 3 and a height that is 5 times the radius.

A: Radius = 3 , Height =3×5= 15Lateral surface area is thre area of sides excluding area of the…

Q: If 1200 cm? of material is available to make a box with a square base and an open top, what is the…

A: according to our guidelines we can answer only first question and rest can be reposted.

Q: An open box is made from a 16 inch by 16 inch piece of cardboard by cutting equal squares from each…

A: This question is based on application of derivative.

Q: Cone A has a radius 12 inches and Cone B has a radius of 30 inches. If the cones are similar and the…

A:

Q: An open-toped rectangular dumpster that is twice as long as it is wide and can hold 12y cubic yards…

A:

Q: What is the maximum area of a rectangle that can be inscribed in a right triangle with a base 8 cm…

A: The rectangle which can be inscribed in a right triangle with base 8 cm and height 6  cm.

Q: A rectangle with sides measuring x in. and 4x-1 in. has an area of 663in.^2. What are the dimensions…

A:

Q: A box with no lid is made by cutting 4 squares of side lenght x from each corner of an 18 cm by 35…

A: After cutting side length x from each side length be l  , l=18-2x breadth be b , b=35-2x height be h…

Q: From a 50-cm-by-50-cm sheet of aluminum, square corners are cut out so that the sides can be folded…

A:

Q: The Luxor Casino in Las Vegas is a square-based pyramid. The height of the pyramid is 350 ft and the…

A: The objective is to find the air capacity that the building can hold.

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-toped rectangular dumpster that is twice as long as it is wide and can hold 12y cubic yards…

A: Given:An open-toped rectangular dumpster that is twice as long as it is wide and can hold 12y cubic…

Q: An open-top box is to be made from a 37 in. by 27 in. piece of cardboard by removing a square from…

A:

Q: The maximum area of a rectangle whose perimeter is 144cm is ... cm^2

A:

Q: A farmer wants to fence in two rectangular corrals, equal in area, using an inner fence as shown in…

A: Given;

Q: A rectangular building is to be built on a triangular corner lot with the perpendicular sides equal…

A:

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 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 rectangular building is to be built on a triangular corner lot with the perpendicular sides equal…

A:

Q: A box is formed by cutting squares from the four corners of a 8"-wide by 10"-long sheet of paper and…

A: Length of the long sheet L = 10'' Width of the long sheet W = 8'' The side of the square cutting…

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the…

A: Let's find.

Q: Suppose 2700 cm² of material is available to make a box with a square base and open top. a) Show…

A:

Q: (EX) Max wishes to enclose a rectangular garden, using one side of his house as shown below. What is…

A: We use second derivative test to find out dimensions of rectangular garden have maximum area

Q: A carpenter is building a rectangular room with a fixed perimeter of 392 ft. What dimensions would…

A: Let l & b be the length and breadth of the room

Q: A box with square ends of side x and a length L is to be made such that L+4x = 4 meters. The…

A:

Q: A farmer has 20 feet of fencing, and he wishes to make from it a rectangular pen for his pig Wilbur,…

A: Let, width= x, length = y So, total fence needed= 2x+y=20 feet  y= 20-2x

Q: A square piece of green origami paper that is 6 inches on a side is being made into a gift box (with…

A: Maximizing the surface.

Q: Suppose that 404 ft of fencing are used to enclose a corral in the shape of a rectangle with a…

A: Area of the shape=Area of the semicircle+Area of rectangle .Area of semicircle=πx22x12…

Q: A rectangular building is to be built on a triangular corner lot with the perpendicular sides equal…

A:

Q: Suppose an open box with a rectangular base is to be constructed from a rectangular piece of…

A: To find the maximum possible volume of the box in cubic inches

Q: Three sides of a trapezoid are 8 inches in length. How long must the fourth side be, so that the…

A: Given: Three sides of a trapezoid are 8 inches in length. Let the fourth side of trapezoid be 8+2x…

Q: A farmer has 2, 000 feet of fence and wishes to build two identical rectangular enclosures, as in…

A: Given query is to find the dimensions of the sides to maximize the area.

Q: A Norman window has the shape of a rectangle surmountedby a semicircle. (Thus the diameter of the…

A: A Norman window has the shape of a rectangle surmountedby a semicircle. Let length of rectangle =2y…

Q: The sum of the dimensions of a box with a sqaure base is 48 m. Find the maximum volume of the box.

A: Volume

Q: Find the dimensions of the rectangle in the figure shown below that will give the maximum area, if…

A:

Q: A cone has a volume that is 350 cubic meters. What is the volume of a similar cone that is twice as…

A: Given, Volume of 1st cone = 350 cubic meters To find the volume of a similar cone that is twice as…

Q: A rancher has 240 feet of fencing with which to enclose two adjacent rectangular corrals (see…

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: find the lenght and width of a rectangle that has the given perimeter and a maximum area perimeter:…

A: We have to find the lenght and width of a rectangle that has the given perimeter and a maximum…