A plastic right cylinder with closed ends is to hold 1000 cubic centimeters of oil. If there is no waste in construction,find the dimensions that will minimize the cost of the plastic to manufacture the can and. What is the ratio of the height to the radius that minimizes the cost?

A plastic right cylinder with closed ends is to hold 1000 cubic centimeters of oil. If there is no waste in construction,find the dimensions that will minimize the cost of the plastic to manufacture the can and. What is the ratio of the height to the radius that minimizes the cost?

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids

Section: Chapter Questions

Problem 79A

See similar textbooks

Related questions

Q: Suppose Hayley wants to mail a poster inside a cylindrical container. To mail a cylindrical package…

A: Surface area of cylinder=2πr2+2πrl

Q: An open rectangular box with square ends to hold 6400 cu ft, is to be built at a cost of $75 per sq…

A: Given that, An open rectangular box with square ends to hold 6400 cu ft. Thus, V= x2 y. 6400 = x2y…

Q: suppose that a can has a radius of 0.8 inches and a height of 3.2 inches how much soup would be able…

Q: An open rectangular box with square ends to hold 6400 cu ft., is to be built at a cost of $0.75 per…

A: The rectangular box is square at base and opened at top.So we will not be involving top of the box…

Q: . The sides of a cube are found to be 6 feet in length with a possible error of no more than 1.5…

Q: Find the minimum cost of a rectangular box that is three times as long as it is wide and which holds…

A: Given that length is three times as long as width so let width be x then length will be 3x let…

Q: A wire 7 meters long is cut into two pieces. One piece is bent into a equilateral triangle for a…

Q: A hollow conical piece is to be fabricated using a metal sheet. The diameter of the cone’s base is…

A: Given : A hollow conical piece is to be fabricated using a metal sheet. The diameter (d) of the…

Q: A rectangular box is to have a square base and a volume of 63 ft3. If the material for the base…

Q: If a spherical tank 4 m in diameter can be filled with a liquid for $250, find the cost to fill a…

Q: We want to build a box whose base length is 6 times the base width and the box will enclose 20in³.…

Q: A Farmer Wants To Enclose A Rectangular Area Along A Highway. The Fencing Along The Highway Will Be…

Q: Calculus 11th Edition - Ron Larson Please assist with the question below. Please show &…

Q: A fence is to be used to entirely enclose a rectangular plot of land with an area at 1600 ft.² It…

A: To show that a 40ft by 40ft rectangle will require the least amount of fencing to enclose the given…

Q: How tall should the file be to maximize the volume that it can hold?

Q: Suppose that the radius and height of a cylinder must add to be 15 cm. What radius and height will…

Q: The top and bottom margins of a poster are each 12 cm and the side margins are each 8 cm. The area…

A: 5. Notice that the dimensions of the poster are: Length = x +16, Width = y +24 Area of the Printed…

Q: A cosmetics company is determining the price of the package they will use for their new line of eye…

A: The given question can be solved as shown in step2

Q: A rectangular parking area measuring 5000 ft? is to be enclosed on three sides using chain-link…

A: The explanation of answer as follows

Q: A box with a square base and a closed top has a volume of 20 cubic ft. the cost of material for the…

A: Given: Volume of square base = 20 cubic feet.…

Q: a square park of length 40 m has a concentric square with sides 35 m inside it find the cost of…

A: find the cost of cementing the space between them if the rate of cementing is rs 50 per sq m.

Q: A box with a square base and open top must have a volume of 4000 cm. Find the dimensions of the box…

Q: If a closed tin can of volume 16x cubic inches is to be in the form of a right circular eylinder,…

Q: A semi-circle of radius 14 cm is formed from a piece of wire. If it is bent into a rectangle whose…

Q: The total surface area of an industrial cylindrical autociave is to be limited to 20m2. If it is…

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

Q: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide…

Q: The sides of a cube are found to be 6 feet in length with a possible error of no more than 1.5…

Q: An open-top rectangular box is being constructed to hold a volume of 350 in. The base of the box is…

A: Given : an open top rectangular box is being constructed to hold a volume of 350 in3, the base of…

Q: A hole in the side of a large metal tank needs to be repaired. A piece of rectangular sheet metal or…

A: Sol :- Given Area (A)=16 ft2 let w = width…

Q: A rancher has 240 ft of fencing with which to build a rectangular corral alongside an existing…

A: We know, in rectangle, pair of opposite sides are equal.In rectangular corral, let length of equal…

Q: You want to frame a collage of pictures with a 9-ft strip of wood. What dimensions will help you…

A: Let us assume that the frame is rectangular and the length be x and width be y. The perimeter of the…

Q: A company manufactures plastic buckets that are shaped like cylinders without a lid. WHich will cost…

A: It is given that the bucket manufactured by the company are cylindrical in shape without a lid…

Q: A farmer wants to fence an area of 37.5 million square feet in a rectangular field and then divide…

Q: The cost of producing an ordinary cylindrical tin can is determined by the materials used for the…

A: Given: Volume =1000 cm3 Volume of cylindrical tin V=πr2h then, πr2h=1000…

Q: A box with a volume of 512cm3 is to be constructed. The sides of the box cost 2 cents per cm2, and…

A: Given the volume of the box is

Q: The total surface area of an industrial cylindrical autoclave is to be limited to 20 m². If it is…

A: Total surface area of the cylinder given = 20 m2Formula for calculating the surface area of the…

Q: a plastic right cylinder with closed ends is to hold v cubic feet. if there is not waste in…

A: Let r and h, in feet be radius and height of cylinder. Volume of cylinder is V cubic feet.

Q: A one compartment vertical file is to be constructed by bending the long side of an 8 in. by 12 in.…

A: The plastic sheet has dimension 8 in. by 12 in. Let x be the height of the compartment file which is…

Q: 2 ends

Q: The ratio of the volume to the lateral area of a right circular cone is 3:1. If the altitude is 15…

A: calculate the ratio of the slant height to the radius .

Q: A rectangular box is to have a square base and a volume of 20 ft³. If the material for the base…

A: Given, Rectangular box is to have a square base and a volume of 20 ft3 The material for the base…

Q: Suppose we want to build a cylinder that has a volume of 100 cubic centimeters. Find the radius and…

A: We have volume as constant, so we can find relation between the radius and height and use that…

Q: A cylindrical metal container, open at the top, is to have a capacity of 24π in3. The cost of…

A: Since, the Volume of a cylindrical container=πr2hand the capacity of container=24π…

Q: A rectangular storage container with an opentop is to have a volume of 10 m. The length of its base…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: A cylindrical can is to be made to hold 2200 cubic inches of oil. Find the radius and height of the…

Q: A closed tin can having a volume of 27 in^3 is to be in the form of a right- circular cylinder. If…

A: Volume of the tin is 27in3.The circular top and bottom are cut from square pieces of tin.To Find:…

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

Concept explainers

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.

Question

Can you please answer this question and show all of the steps and say the correct letter

A plastic right cylinder with closed ends is to hold 1000 cubic centimeters of oil. If there is
no waste in construction,find the dimensions that will minimize the cost of the plastic to
manufacture the can and. What is the ratio of the height to the radius that minimizes the
cost?

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

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Matrix Operations$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

A cylindrical orange juice container has metal bases of radius length 1 in. and a cardboard lateral surface 3 in. high. If the cost of the metal used is 0.5 per square inch and the cost of the cardboard is 0.2 cent per square inch, what is the approximate cost of constructing one container? Use 3.14.
The tin can shown at the right has the indicated dimensions. Estimate the number of square inches of tin required for its construction. HINT: Include the lid and the base in the result.
The gasoline tank on an automobile is box-shaped with dimensions of 24 in. by 20 in. by 9 in. If 1 ft3 corresponds to 7.5 gal of gasoline, What is the capacity of the automobiles fuel tank in gallons?
a For the through in the shape of half-cylinder, find the volume of water it will hold Use 3.14 and disregard the thickness b If the trough is to be painted inside and out, find the number of square feet to be painted Use 3.14.
A goat is tethered to a barn by a 12-ft chain. If the chain is connected to the barn at a point 6 ft from one end of the barn, what is the area of the pasture that the goat is able to graze?