A piece of wires 10 m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut so that the total area enclosed is maximum ?

Q: A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is…

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Q: A packaging company is going to make open-topped boxes out of 20 cm by 20 cm rectangles of cardboard…

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Q: An open box will be made by cutting a square from each corner a 5-ft by 8-ft piece of cardboard and…

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Q: What is the longest dimension of an open top rectangular box of greatest volume that can be…

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Q: An open box will be made by cutting asquare from each corner of a 3-ft by 8-ft piece of cardboard…

A: Consider the "x" represent the side length of the cut-out square.  The length is 8 ft and the…

Q: A box with a square base and with height is to be constructed so that it has a volume of 1000 cubic…

A: A box with a square base and with height is to be constructed so that it has a volume of 1000 cubic…

Q: A pool in the shape of a right rectangular prism is 15 m long, 9m wide, and 2 high. What is the…

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Q: if an open box is to be made using a square sheet of tin, 20 inches by 20 inches, by cutting a…

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Q: A farmer uses 2000 feet of fence to enclose a rectangular region and also to subdivide the region…

A: Let the width of the fence be:  w Let the length of the fence be:  l

Q: A rectangular square-based open-top container is to be made so as the surface area equals 24 m2.…

A: let the dimensions of container according to question are :lengh=a,width=a, and height =hsurface…

Q: A square piece of cardboard of side a is used to make an open-top box by cutting out a small square…

A: Since, a square piece of cardboard of side 'a' is used to make an open-top box by cutting out a…

Q: A semi-elliptical goblet has a depth of 4 inches and its round opening has a width of 3 inches. It…

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Q: The Philippine Postal Service will accept a box for domestic shipment only if the sum of its length…

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Q: A piece of wire 10 m long is cut into two pieces. One piece is bent into a square and the other is…

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Q: Find the minimum cost of a rectangular box of volume 180 cm3 whose top and bottom cost 8 cents per…

A: Cost can be minimised by finding out the partial derivatives

Q: A piece of wire 10 m long is cut into two pieces. One piece is bent into a 30°-60°-90° triangle and…

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Q: A long rectangular sheet of metal 30 inches wide is to be made into a gutter by turning up strips…

A: Let the length of the vertical strips along the tow sides is x inches. Then the length of the base…

Q: What are the dimensions of a rectangular wall that can be constructed with 81 feet of brick that…

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Q: An оpen box is to be made from a 6 ft by 16 ft rectangular cardboard by cutting out equal squares…

A: We can find the maximum volume of the box as below

Q: A jewelry box with a square base is to be built with silver plated sides, nickel plated bottom and…

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Q: Norman builds a rectangular pig pen with two parallel partitions using 150 meters of fencing…

A: let the length of Pig pen be "a"width be " b" Perimeter=150 metresPerimeter = 2(a+b)…

Q: A box with an open top is to be constructed from a square piece of cardboard, 3 feet wide, by…

A: Four square pieces at the corners of a square cardboard of size 3 × 3 feet.  And it was made into a…

Q: A farmer wants to secure a certain part of his land. Calculate the maximum area of a rectangular lot…

A: Given: total length of fencing material of rectangular plot = 1000m

Q: A farmer wants to construct a rectangular pigpen using [ 100 ] ft of fencing. The pen will be built…

A: Given data: The total length of fencing is 100 ft. Consider the length of AB=x. Consider the length…

Q: If the length of three sides of a trapezium other than base are equal to 10 cm, then find the area…

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Q: With a rectangular piece of metal 150cm by 200cm, cut out squares from each corner in order to…

A: I use second derivative method to find dimensions of box where volume maximum

Q: a wire measuring 12 ft long is cut into two pieces. once piece is to be bent into a square and the…

A: The perimeter of a square is: Perimeter=4a Area of a square is: Area=a2 Where a is the edge of the…

Q: A manufacturer wants to design an open box having a square base and a surface area of 244 square…

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Q: A closed box with square base and vertical sides is to be made from 150 square feet of cardboard.…

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Q: A 63-inch by 168-inch pieceof cardboard is used to make an open-top container by removing a square…

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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: A farmer has 400 ft of fencing with which to enclose a rectangular field adjacent to anexisting…

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Q: from a piece of cardboard that is 24 cm by 48 cm ,cut equal squares out of the corners . fold up the…

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

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Q: A piece of sheet metal is rectangular, 5 feet wide and 8 feet long. Congruent squares are to be cut…

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Q: A pressure tank has a hemispherical base surmounted by a right circular cylinder and which in turn…

A: we know that volume of semi sphereV1, volume of right circular coneV2 and volume of cylinder V3 is…

Q: A 10-ft wire is to be formed into an equilateral triangle and a square. What is the measure of the…

A: Given;+ A 10-ft wire is to be formed into an equilateral triangle and a square. To find What is the…

Q: A piece of wiren 10 m long is cut into two pieces. One piece is bent into a square and the other is…

A: Length of the wire is 10 m. Let the length used for the square be x. Thus, the length used for…

Q: A piece of wire 14 m long is cut into two pieces. One piece is bent into a square and the other is…

A: the total length of a wire is 14m  let the length of a square be x m so, the length of a circle will…

Q: A metallic sheet is of rectangular shape with dimensions 1m x 2m. From each of its corners, a square…

A: Given height = 8 cm So, given that each one of its corners a square of side 8 cm is cut off  now,…

Q: A box with an open top is to be constructed from a square piece of cardboard, 24 inches wide, by…

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Q: What the maximum area of a triangle which is inscribed in a circle of radius 4cm and one of its…

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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 farmer with 750 ft of fencing wants to enclose a rectangular region and then divide it into four…

A: Solve for the lager rectangle dimension and area of large rectangle

Q: A company that manufactures dog food wishes to pack the food in closed cylindrical tins. What should…

A: Use application of derivative concept. volume of cylinder and total surface area of cylinder…

Q: A 60 m long pipe of metal is cut into two pieces. One piece is used to form a square and the other…

A: Perimeter of square =4a 4a=x Perimeter of triangle =3b 3b=60-x b=(60-x)/3

Q: An open topped box is to be made from a rectangular piece of metal 18cm x 48 cm by cutting off…

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