A rectangular package to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 72 inches (see figure). Find the dimensions of the package of maximum volume that can be sent. (Assume the cross section is square.) y =

Q: An open box with a square base is to have a volume of 12ft^3. find the box dimensions that minimize…

A: The volume of a rectangular prism(cuboid) = l×b×h Let y = measurement of each side of the base, h =…

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A: To find the dimensions of the rectangle of largest perimeter that can be inscribed in the…

Q: A paper cup is to be made in the shape of a cone, having volume 3 ounces. What should the radius and…

A: Let Volume = V  Radius = r inch. Height = h inch.  Volume of cone V=13πr2hh=9πr2    ....(1)

Q: An oocyte is an immature reproductive cell found in many sexually reproducing organisms. A crawfish…

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Q: A waterway in a theme park has a semicircular cross section with diameter 11 ft. The boats that are…

A: Consider the figure for the water way and the boat. The circumference of the boat is the equation of…

Q: Find the length L and W (with W(less than or equal to) L) of the rectangle with perimeter 48 that…

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Q: In constructing an open rectangular box from 867 ft of material, what dimensions will result in a…

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Q: You are to construct an open rectangular box from 12 ft2 of material. What dimensions will result in…

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Q: Find the maximum volume of a cylindrical soda can such that the sum of its height and its…

A: we have to find the maximum volume of a cylindrical soda can such that the sum of its height and its…

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: Fruit juice will be packaged in cylindrical cans with a volume of 40 in each. The top and bottonm of…

A: Fruit juice will be packaged in cylindrical cans with a volume of 40 in3 each. The top and the…

Q: A Norman window has the shape of a rectangle surmounted by a semicircle. Find the dimensions of a…

A: Given that the perimeter is fixed.Let us assume that the length of the rectangle part which is also…

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

A: Find the maximum volume  by derivative

Q: we have 27ft squared of material to build a box of maximum volume with a square base and no top.…

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Q: In constructing an open rectangular box from 192 ft? of material, what dimensions will result in a…

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Q: DAUST's students plan to design a closed box with a square base and a surface area of 90 cm2 for…

A: If the side of square base is 'a'cm and length is 'b'cm Than surface area will be a2b

Q: Consider an open top rectangular box with a square base. Find the dimensions of the box for which…

A: S

Q: An open box is to be made from a 3-ft by an 8-ft rectangular piece of sheet metal by cutting out…

A: An open box is to be made from a 3-ft by an 8-ft rectangular piece of sheet metal by cutting out…

Q: A cardboard box without a lid is to have a volume of 4000cm3. Find the minimum amount of cardboard…

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: The diagram shows a square prism with cross-section x units by x units, and length (9- 2x) units.…

A: We know that the volume of a square prism is equal to its base area X the height. first of all we…

Q: A storage tank is designed by rotating y = x² + 1; about the x- axis, y- axis, line x = 2, and…

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Q: the maximum area for the rectangular whic

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Q: A right circular cone has a base diameter of 24 cm. The maximum area of parabolic segment that can…

A: Use the following formulae, to obtain the solution. Area of Parabolic Segment=23bhVolume of the…

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A: Given;

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

A: Given volume of the can is (128)πcm3 Let height=h radius=x

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A: we use formula   surface Area of cone =  πrl + πr2

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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 right triangle with hypotenuse of 5/3 inches is revolved about one of its legs t generate a cone.…

A:

Q: Find the dimensions of the rectangular box, open at the top, which has a minimum surface area if the…

A: Let us consider the width, length and height of the rectangular box are x, y and z respectively.…

Q: Define the livable space of a building to be the volume of space in the building where a person 6…

A: As given that height of the rectangular box= 6 ft. (according to the height of person) Length of the…

Q: A thin-walled cone-shaped cup (see figure) is to hold 36t cm of water when full. What dimensions…

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Q: D. A Box with linear dimensions three times the box above... Surface Area = Volume = E. A Sphere…

A: The given cube has surface area 150 cm2 For part D: To find surface area and volume of box with…

Q: A parcel delivery service will deliver a package only if the length plus the girth (distance around,…

A: Let the side of the rectangular box is l, b and h.  Maximum possible dimension is  2l + 2b + h = 108…

Q: The volume of a closed cylinder tank is 11.3 m3 . If the total surface area is a minimum ,what is…

A: Introduction :

Q: A farmer wants to make a rectangluar enclosure using a wall of a barn as one side and 160 ft of…

A: Let x ,in feet, be the length of side of rectangular enclosure which is along the wall of barn and y…

Q: Find the minimum cost of a rectangular box of volume 100 cm³ whose top and bottom cost 6 cents per…

A:

Q: The base of a rectangular prism shaped aquarium without a lid is made of slate and the sides are…

A: Given V=96 m3 Let the dimension is x, y and z Hence, Volume is given by V=xyz......1 The equation…

Q: | We have 48 m? of material to build an open box with a square base. nine the dimensions of the box…

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

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

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Q: A light bulb is designed by revolving the graph of y = the surface area of the bulb and use the…

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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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Maximization

Have you ever seen a bridge in the shape of a parabola? Where is its maximum on the bridge? The maximum of that bridge is the highest point on that bridge. The process of finding the maximum of the bridge here is called the maximization.