A 10 m? plastic is to be used to form a hollow cylinder that has a circular base and| an open top. Determine the dimension of the cylinder that can produce the maximum volume and find the value of the maximum volume.

A 10 m? plastic is to be used to form a hollow cylinder that has a circular base and| an open top. Determine the dimension of the cylinder that can produce the maximum volume and find the value of the maximum volume.

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

Section9.3: Cylinders And Cones

Problem 6E: Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a...

See similar textbooks

Related questions

Q: A sphere has a radius of 6 feet. What are the dimensions of the cylinder with the greatest volume…

A: Given: Radius of sphere = 6 feet. To find: The maximum volume of the cylinder

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

Q: A long metal sheet with a width of L meters is formed into a gutter by bending up two of its sides…

A: We will use the basic knowledge of 3D solid geometry and applied differential calculus to answer…

Q: Find the maximum volume of sphere that may be completely submerged in a cone of height 5 m. Express…

Q: A rectangular storage area is to be constructed along a side of a building. A security fence is…

A: Given Take length of side parallel to building = y length of side perpendicular to building = x…

Q: A manufacture wants to design an open box having a square base and a surface area of 256 square…

Q: A sheet of cardboard 16 in. square is used to make an open box by cutting squares of equal size from…

A: Given, a sheet of cardboard 16 in. square is used to make an open box by cutting squares of…

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: find the maximum valume of a cone given that the sum of the radius and height of the cone is 15 cm.

Q: what are the dimensions of the right hexagonal prism of minimum surface whose volume is 36 cubic…

A: This is a problem of optimization.

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: An open box is to be made from a 15 ft by 40 ft rectangular piece of sheet metal by cutting out…

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

Q: The circumference of a sphere is measured to be 84 cm with a possible error of 0.5 cm. a. What is…

Q: A square sheet of metal has squares cut from its corners as shown. A What sized square should be cut…

Q: Jim wants to build a rectangular parking lot along a busy street but only has 1,600 feet of fencing…

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: An open-top bin is to be made from a 15-centimeter by a 40-centimeter piece of plastic by removing a…

A: Assume that side of square which should be cut from each corner is a.Given the dimension of piece of…

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

Q: A rancher has 400 feet of fencing with which to enclose two adjacent rectangular corrals (see…

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 Plastic flower pot in the form of an inverted pyramid has a height of 6 inches whose four edge's…

A: Solved below

Q: Find the dimensions of the closed rectangular box of largest volume with surface area of 16 m². What…

Q: An open-top crate is to be constructed with 54 ft2 of material available to use. The length of its…

A: Let width = x So, length = 2xLet height = hVolume of the crate = V = (x)(2x)(h)= 2hx^2

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

Q: An open storage bin with a square base and vertical sides is to be constructed from a given amount…

Q: Postal regulations require that for priority mail the length and girth of a rectangular parcel…

Q: What is the maximum size of the window frame you can create with 20 feet of materials? The window…

A: To Find: The maximum size of the window frame you can create with 20 feet of materials.

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 rancher has 200 feet of fencing with which to enclose two adjacent rectangular corrals (see…

A: Total fencng = 200 feetTotal fencing = 4x+3y=200 feet — (i)Area = 2x×yFrom eqn - i - y =200-4x3Area…

Q: A rectangular box is to have a base whose width is twice the length and is to have no top. If the…

A: Given, A rectangular box is to have a base whose width is twice the length and is to have no top.…

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

Q: Q2. Calculate the maximum volume that can be got from a rectangular sheet (4cmx3cm). The sheet is…

A: To solve this problem, we have to obtain the volume of the open box as a function of some variable x…

Q: An open box is to be made from a 33 ft by 88 ft rectangular piece of sheet metal by cutting out…

A: You have asked multiple questions, so we will solve the first question for you. The rest can be…

Q: |An open storage bin with a square base and vertical sides is to be constructed from a given amount…

A: According to the question, Let the length, breadth and depth of the open tank be x, x and y,…

Q: Find the maximum area that can be formed by a series of small pens next to a river with separate…

A: The area of a rectangle is the product of its length and breadth. For a parabola of the form…

Q: A window is in the shape of a rectangle surrounded by a semicircle. If the perimeter of the window…

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: A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular…

A: Given: The total perimeter is 16 feet. The given window is formed by adjoining semicircle to the top…

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

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

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

Q: EA farmuur wants to build ariding arena in the Shape of a rectapule topped tby two Simixirelesa find…

A: Consider the given information.

Q: A close rectangular box where length is double its width has a total surface of 300 square inches.…

Q: A farmer would like to construct a cage to separate farm animals. He has 600 meters of materials to…

Q: An open box is to be made from a 33 ft by 88 ft rectangular piece of sheet metal by cutting out…

A: Solve the given problem.

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: find the maximum volume of a rectangular box that a post office will accept for delivery of the sum…

Question

A 10 m? plastic is to be used to form a hollow cylinder that has a circular base and|
an open top. Determine the dimension of the cylinder that can produce the
maximum volume and find the value of the maximum volume.

Expert Solution

This question has been solved!

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

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Step by step

Solved in 5 steps with 5 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

How are the absolute maximum and minimum similar to and different from the local extrema?
A cylindrical container has a volume of 84 cubic inches and a radius of 3 inches. Find the height of the container.
The box with dimensions indicated is to be constructed of materials that cost 1 cent per square inch for the lateral surface and 2 cents per square inch for the bases. What is the total cost of constructing the box?
Suppose that r=12 cm and h=15 cm in the right circular cylinder. Find the exact and approximate a lateral area. b total area. c volume.
A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Compute the volume of a prism with a base area of 220.0 square centimeters and a height of 7.600 centimeters.
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Find the volume of a right circular cylinder that has a height of 4,600 inches and a base area of 53.00 square inches.