Answered: An open box with a square base is to…

An open box with a square base is to have a volume of 12ft^3. find the box dimensions that minimize the amount of material used

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.1: Prisms, Area And Volume

Problem 27E: The box with dimensions indicated is to be constructed of materials that cost 1 cent per square inch...

See similar textbooks

Related questions

Q: A rectangular piece of cardboard is 16 inches by 10 inches. Squares are going to be cut out of the…

Q: A cylindrical container with a circular base and open top must have a volume of 1000 m³. Find the…

Q: A box with a square base and open top must have a volume of 62,500 cm. Find the dimensions of the…

A: Topic- Application of Derivative

Q: Find the minimum cost of a rectangular box of volume 140 cm³ whose top and bottom cost 2 cents per…

Q: A box with a square base and open top must have a volume of 55296 cm. We wish to find the dimensions…

Q: The rectangular bird sanctuary with one side along a straight river is to be constructed so that it…

Q: A rectangular box having a square base and open at the top is to have a capacity of 16,823 cubic…

A: suppose the side of the box = x cm.height= h cm.Given : Volume = 16823 cc

Q: You have been asked to design a one-liter can shaped like a right circular cylinder. What dimensions…

Q: A landscape architect wishes to enclose a rectangular garden of area 1000 m2 on one side by a brick…

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 parcel of land is in the form of a rectangle. Its area is 40 square meters. What should be its…

A: Let x and y , in meters be the length and width of the rectangular piece of land. Its area is 40…

Q: a box with a square base and an open top must have a volume of 4000 cm^3. find the dimensions of the…

A: Let the length of each side of the base= x Height=y So

Q: A metal cylindrical container with an open top is to hold one cubic foot. If there is no waste in…

A: Given: Volume = 1 cubic foot

Q: Find the dimensions of a cylindrical can with a bottom but no top of volume 4 m3 that uses the least…

A: To Find: Dimension of a cylindrical can with a bottom but no top of volume 4 m3that uses the least…

Q: Find the dimensions of a cylinder of volume 5 m3 of minimal cost if the top and bottom are made of…

A: In order to solve this problem, first we need to find the expression that represents the total cost.…

Q: A rectangular solid (with a square base) has a surface area of 337.5 square centimeters. Find the…

Q: A box with a square base and open top must have a volume of 78732 cm'. We wish to find the…

A: We know that the volume of the box with square base x cm and height h cm is given byV=x2hThe amount…

Q: A can in the shape of a right circular cylinder is required to have a volume of 500 cubic…

A: The radius= r Height= h So the volume is: V=πr2h500=πr2hFrom here we get:h=500πr2

Q: ) A company manufactures cylindrical metal drums with open tops with a volume of lcubicmeter. What…

A: Given that volume=V=1m3what should be the dimensions of the drum in order to use the least amount…

Q: A rectangular plot of playground with a 500 m^2 area is to be surrounded by a fence, with an…

Q: A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the…

Q: Find the dimensions of a right circular cylinder of maximum volume that can be inscribed in a sphere…

A: Draw the diagram roughly.

Q: Find the dimensions of a closed rectangular box with a square base and volume 3375 in3 that can be…

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: A poster needs to have 75 square inches of printed material with margins of 5 inches at the top and…

A: Given: Area of rectangular page = 75 square inches Also, we have margins of 5 inches at the top and…

Q: A rectangular box with a square base and no top is to have a volume of 108 cubic inches. Find the…

A: Rectangular box with square base Volume (v) = 108 inch3let base is a x a squareheight = bvolume…

Q: Find the rectangular box of maximum volume if the sum of the lengthsof the edges is 300 cm.

Q: Find the dimensions of the right circular cylinder of greatest volum that can be inscribed in a…

A: Given query is to find the dimensions of a right circular cylinder that can be fit inside a sphere…

Q: A one compartment vertical file is to be constructed by bending the long side of an 8 in. by 14 in.…

Q: To calculate: The dimension of the rectangular solid with a square base that yields the minimum…

A: The rectangular solid has a square base. Let the dimensions of the rectangular solid be x, x and y.…

Q: Determine the dimension of a rectanglular solid with a square base with a maximum volume of its…

A: Volume V=x2y Surface area=2x2+4xy

Q: A poster of area 6000 cm2 has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the…

A: SOLUTION-

Q: A builder intends to construct a storage shed having a volume of 900 cubic feet, and flat roof, and…

Q: A cylindrical can is to have a volume of 400 cubic centimeters. Find the dimensions (height and…

Q: An open box is formed by cutting identical squares from each corner of a 4 inches by 4 inches sheet…

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: Consider a rectangular box B that has a bottom and sides but no top and has minimal surface area…

A: Given information: V=64 m3

Q: The base of an aquarium (in the shape of a cuboid) with given volume V is made of slate and the…

Q: A box with a square base and open top must have a volume of 42592 cm. We wish to find the dimensions…

A: Let the height of the box is h and the base of the box is square of length x. so the volume of the…

Q: Find the dimensions of a cylinder of volume 3 m³ of minimal cost if the top and bottom are made of…

Q: A company manufactures cylindrical metal drums with open tops with a volume of lcubicmeter. What…

A: Let the radius of the cylinder is =r and the height of the cylinder is =h The volume of the cylinder…

Q: A piece of wire 5 meters long is cut into two pieces. One piece is bent into a square and the other…

Q: A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the…

A: Consider a box with square base and open Top and have a volume of 4000 cubic centimeters. Let the…

Q: Find the minimum cost of a rectangular box of volume 200 cm³ whose to

Q: Find the minimum amount of thin sheet that can be made into a closed cylinder having a volume of 108…

A: Topic: calculus

Q: You have been asked to design a 1L oil can shaped like a right circular cylinder with open top. What…

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

Q: Brittany needs to construct a cylinder from a single sheet of metal with a perimeter of 2,148 mm.…

A: Given that a single sheet with perimeter 2148 mm.

Q: A rectangular box without a lid is made with a material cost of $10.00. If the material for the…

A: Using AM GM INEQUALITY

Question

An open box with a square base is to have a volume of 12ft^3.

find the box dimensions that minimize the amount of material used

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1: Formulate Volume

VIEW

Step 2: Formulate Surface Area

VIEW

Step 3: Get h in terms of y

VIEW

Step 4: Surface Area in single variable y

VIEW

Step 5: Finding minima using derivatives

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Find the rectangular box of maximum volume if the sum of the lengthsof the edges is 300 cm.
Find the dimensions of a closed rectangular box with a square base and volume 3375 in3 that can be constructed with the least amount of material.
An open-top bin is to be made from a 15-centimeter by a 40-centimeter piece of plastic by removing a square from each corner of the plastic and folding up the flaps on each side. What size square should be cut out of each corner to get a bin with the maximum volume?
A 63-inch by 168-inch pieceof cardboard is used to make an open-top container by removing a square from each corner of the cardboard and folding the flaps on each side. What is the area of the square that should be cut from each corner to get a container with the maximum volume?
A landscape architect wishes to enclose a rectangular garden of area 1000 m2 on one side by a brick wall costing $90/m and on the other three sides by a metal fence costing $30/m. Which dimensions minimize the total cost?
What are the dimensions of a closed rectangular box that has a square cross section and a capacity of 125 cubic inches and is constructed using the least amount of material?
A box with a square base and an open top must hold 32 cubic inches of volume. Find the dimensions of the box that require the least amount of material (ie minimize the surface area of the topless box). Do not worry about the thickness of the material of the waste from construction.
A beverage company manufactures 2-liter pineapple juice to be packaged in cylindrical cans made of tin. In order to save the container, the surface area of this cylinder should be minimized. Determine the dimensions (height and radius in cm) in order to achieve this.
You have been asked to design a 1L oil can shaped like a right circular cylinder with open top. What dimensions will use the least material?
A poster needs to have 75 square inches of printed material with margins of 5 inches at the top and bottom and 2.25 inches on either side. Find the overall dimensions that minimize the total poster area.
A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the box that minimize the amount of material used. ____sides of base cm ____height cm
What size square should be cut out of the index card in order to maximize the volume of the box?