Answered: A cylindrical can, open at the top, is…

A cylindrical can, open at the top, is to hold 500 cm of liquid. Find the height, h, and the radius, r, that minimize the amount of material needed to manufacture the can.

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.CR: Review Exercises

Problem 13CR: The radius length of the base of a right circular cylinder is 6 in. The height of the cylinder is 10...

See similar textbooks

Related questions

Q: A company wants to manufacture cylindrical aluminum cans with a volume of 1000 cm3. What should be…

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

Q: A cylindrical can of height h and radius r is to be made with a fixed volume V. Show that the area…

Q: Find the volume of a hemispherical shell having outer radius a and inner radius b if the density…

A: Mass density is defined as the mass per unit volume. gm/cm3 is, therefore, a unit of mass density.…

Q: Consider a right circular cylinder open top tin can with volume 1000 cm3. Suppose R and H are the…

A: Please refer the attached image for complete solution. THANK YOU.

Q: The volume of the closed cylindrical tank is 11.3 cubic meter, if the total surface area is a…

A: Given; The volume of the closed cylindrical tank is 11.3 cubic meter.

Q: A cylindrical drum is to be manufactured from a synthetic material and is to hold 547 m³ of liquid.…

A: The solution is given below in the next step:

Q: Find the dimensions of a cylindrical can with a volume of 666 in^3 that minimizes the surface area.…

A: To find the dimensions of a cylindrical can with a volume of 666 in3 that minimizes the surface…

Q: A conical vessel is 12 m across the top and 15 m deep. If it contains water to a depth of 10 m, find…

A: We need to consider a section and then integrate accordingly.

Q: Consider a right circular cylinder open top tin can with volume 1000 cm3. Suppose R and H are the…

A: Given that: Volume of cylinder = 1000 cm3

Q: The total surface area of an industrial cylindrical autoclave is to be limited to 20m^2. If it is…

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

Q: A sphere has a radius of 5.81 in., with a possible error of ± 0.003 in. Estimate the maximum error…

A: For a sphere of radius r the expression for the volume is V=43πr3. The error in r is denoted as ∆r.…

Q: A cylindrical can without a top is made to contain 381 in³ of liquid. Find the dimensions that will…

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

Q: A firm wants to build cylindrical containers to transport its cargo. The volume of each container…

Q: A hemispherical tank has a radius of 13ft. Given that the water weighs is 62.5lb/ft3, find the work…

Q: A cylindrical can, open at the top, is to hold 200 cm³ of liquid. Find the height, h, and the…

A: Consider the given: The given volume of the cylinder is 200 cubic cm. V=πr2h200=πr2hh=200πr2 Find…

Q: A closed cylindrical tank is to be made from a material 230.91m2 in area. If the volume of the…

Q: A flexible tube of length 4 m is bent into an L-shape. Where shouldthe bend be made to minimize the…

A: A flexible tube of length 4m is bent into an L-shape. Let x,y be the length of sides of L-shape.…

Q: 21. The volume of the closed cylindrical tank is 11.3 m3. If the total surface area is a minimum,…

A: The volume, V of a cylinder is calculated using the formula, V=πr2h. The surface area, A of a…

Q: A company is constructing an open-top, square-based, rectangular metal tank that will have a volume…

Q: Determine the dimensions of a rectangular box, open at the top, having volume V, and requiring the…

A: Let Length=xWidth=yHeight=z Then volume of the box is v=xyzz=vxy…

Q: You want to produce a cylindrical water container with a capacity of 350mL. What dimensions will…

A: We have to find the dimensions of the cylinder.

Q: Find the dimensions of a cylinder of volume 1 m 3of minimal costif the top and bottom are made of…

A: Given: Find the dimensions of a cylinder of volume 1 m 3of minimal cost if the top and bottom are…

Q: A cylindrical can, open at the top, is to hold 600 cm³ of liquid. Find the height, h, and the…

Q: The base of a solid is the unit circle x^2+y^2=1 , and its cross sections perpendicular to the…

Q: Show that it is not possible to design a cylindrical can (with top and bottom) of volume 400 cubic…

Q: A closed top cylinder can is to have a volume of 250in^3 a) What dimensions (radius and height)…

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

Q: A pharmaceutical company wants to manufacture cylindrical aluminum cans with a volume of 1000 cm3 (1…

A: Since we know that, Surface area of cylinder, S=2πrh+2πr2 ...(1) And volume of cylinder, V=πr2h…

Q: A spherical gas reservoir has a circumference of 10 ft. This reservoir is to be holed 3 feet below…

A: Given: Circumference of spherical reservoir is, C1=10 ft. Circumference of cylindrical hole is,…

Q: A manufacturer of food-storage containers makes cylindrical can with a volume of 500 milliliters.…

A: A manufacturer of food-storage containers makes cylindrical can with a volume of 500 milliliters.

Q: A cylindrical container that is open at the top is to be made from two kinds of material. The…

Q: A MANUFACTURER NEEDS TO MAKE A CYLINDRICAL CAN THAT WILL HOLD 1.5LITRES OF LIQUID . Determine the…

A: Given : volume of the cylinder π r2h Surface area = 2 π r h + 2 π r2 To Minimize: Surface…

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 closed cylindrical tank of maximum volume is to be constructed. With only 381.7 m^2 of material,…

Q: A closed rectangular box with square base is to be constructed. Suppose the volume is 27 cubic cm.…

Q: A manufacturer of food-storage containers makes cylindrical can with a volume of 500 milliliters.…

A: A manufacturer of food-storage containers makes cylindrical can with a volume of 500 milliliters. We…

Q: Consider a right circular cylinder open top tin can with volume 1000 cm³. Suppose R and H are the…

A: We will use derivative to minimize the area.

Q: Suppose a 4-m cylindrical bar has a constant density of 5 g/cm for its left half and a constant…

Q: A cylindrical container that is open at the top is to be made from two kinds of material. The…

Q: A soft-drink company needs to design a cylindrical can that can hold 475 ml of fluid. What are the…

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 storage reservoir with volume 32 m³ needs to be constructed (Figure Q5.c). The reservoir is shaped…

A: A function f(x) will have the maximum value at a point x when the derivative of the function is zero…

Q: Consider a right circular cylinder open top tin can with volume 1000 cm?. suppose R and H are the…

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

Q: A cylindrical can, open at the top, is to hold 700 cm of liquid. Find the height, h, and the radius,…

A: Given, volume of cylindrical can is 700 cm3. height = h radius = r We have to minimize the amount of…

Question

A cylindrical can, open at the top, is to hold 500 cm of liquid.
Find the height, h, and the radius, r, that minimize the amount
of material needed to manufacture the can.
NOTE: Enter the exact answers.
h =
cm
cm

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

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 2 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

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.
For the right circular cylinder, suppose that r=5 in. and h=6 in. Find the exact and approximate a lateral area. b total area. c volume.
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Compute the height of a prism with a base area of 2.7 square feet and a volume of 4.86 cubic feet.
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.
For a right circular cone, the dimensions are r=6 cm and h=8 cm. If the length of the radius is doubled while the height is made half as large in forming a new cone, will the volumes of the two cones be equal?
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.
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?
The radius length of the base of a right circular cylinder is 6 in. The height of the cylinder is 10 in. Find the exact a Lateral area b total area c volume.
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. A solid right cylinder 9.55 centimeters high contains 1910 cubic centimeters of material. Compute the cross-sectional area of the cylinder.
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.
Cycling The Campagnolo Hyperon Ultra Two carbon wheel, which has a diameter of 700 millimeters, has 22 spokes evenly distributed around the rim of the wheel. What is the length of the rim subtended by adjacent pairs of spokes (Figure 15)?
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.