Suppose a cylindrical can is being made to hold 1 liter of oil. Design the can so that the minimum amount of metal can be used. The area of the metal is given by 1000 A=27r27 rh Note that 1L = 1000cc so zr h 1000, h 2

Suppose a cylindrical can is being made to hold 1 liter of oil. Design the can so that the minimum amount of metal can be used. The area of the metal is given by 1000 A=27r27 rh Note that 1L = 1000cc so zr h 1000, h 2

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: The density of a type of stone is 2000 kg/m^3. Find the work needed to build a stone cone with a…

A: Given: The density of the stone is 2000 kg/m3. The radius of the stone cone, r = 100m. And, the…

Q: A cylindrical pop can holds 400 cm³ of pop. How should it be constructed so that minimum amount of…

A: Here the volume of the cylindrical pop is given, that means volume is fixed as 400cm³. Minimum…

Q: A cylindrical container with both ends closed has a radius r cm and a volume 100 cm³. Determine the…

Q: A circular swimming pool full of water has a diameter of 24 ft and the sides are 5 ft high. Set-up…

A: A circular swimming pool full of water has a diameter of 24 ft and the sides are 5ft high.

Q: A closed right circular cylindrical tank made of s inch thick metal has an outer radius of 2 ft and…

A: solution:-(1)outer radius, r=2 ftheight, h=6 ftouter surface area of cylinder= 2πrh+2πr2…

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

Q: By integrating all three surface elements of a cylinder, find the surface area of a cylindrical pie:…

Q: 13 1 y = 1/2x² + ²x² 6x 1 √2 <x< 1 Curved segment rotated about the ox-axis.Calculate the area of…

A: Given that y=12x3+16x ,12≤x≤1

Q: What are the dimensions of the lightest open-top right circular cylindrical can that will hold a…

A: Here we have to find the dimensions of the lightest open-top right circular cylindrical can that…

Q: The volume of a right circular cone of radius a and height y is given by V : ' = ma²y. Suppose that…

A: From the given problem; The expression for the volume of the cone is: V=13πx2y And The volume of the…

Q: The density of a spherical solid of radius 2, centered at the origin, is given by D(ρ) = 4ρ grams…

A: Consider the following figure.We have find the volume of the solid above the plane z = 3.

Q: 5. Find the volume of spherical wedge formed by rotating through an angle of 45 a semi circle of…

Q: A cylindrical tank, shown to the right, has height 8 m and radius 5 m. a. If the tank is full of…

A: Given : (a). height = 8 m radius = 5 m acceleration due to gravity, g…

Q: The surface area of a sphere increases at a rate of 77 m2/sec. Then the rate at which the radius…

Q: The surface area of a sphere increases at a rate of 90 m2/sec. Then the rate at which the radius…

Q: An industrial container is in the shape of a cylinder with hemispherical ends, as shown in the…

A: To Determine: An industrial container is in the shape of a cylinder with hemispherical ends, as…

Q: Suppose a water tank has the shape of a cylinder, with a circular base. The height of the tank is 9…

A: Let height of each strip is dx. Radius =r= 2 is constant. A strip at the x ft height, has to be…

Q: The base of a solid is in the first quadrant bounded above by y = 5 and below by y = √5x between x =…

A: The given curves are y=5, y=5x, x=0, x=5 which forms the base of a solid. The cross section of the…

Q: 3) Calculate the work against gravity to build a box of h=3m with a square base of side 2m made from…

Q: calculate the work required to build a pyramid with a height of 4m and a square base of side length…

A: The density is 600 kg/m^3 and the gravity is 9.8 m/s^2. The product of the force and displacement…

Q: Find the radius ? and height ℎ of a cylindrical can of total surface area 110 cm2 whose volume is as…

A: NOTE: Refresh your page if you can't see any equations. . the surface area of the cylinder is given…

Q: The volume of a right circular cone of radius x and height y is given by V = 1/3πx^2y. Suppose…

A: Solution:Given V=13πx2yTo find dydx at x=4 and y=16Formula:ddx(xn)=nxn-1

Q: When the area between the curve y= x², 0<x<2 and the y-axis is rotated about the y-axis, it forms a…

Q: A cylindrical tank of radius 5 ft and height 9 ft is two-thirds filled with a liquid of weight…

A: Work=Distance*density*volume Distance=9-ydensity=ρvolume=πx2×dyas it is cylinder , x = r…

Q: a closed cylindrical tank 10 ft in height and 4ft in diameter contains water with depth of 3ft and…

A: First, convert dimensions from feet to inches:Height of tank = 10 ft = 120 in, Height of water = 3…

Q: Find the dimensions of a right cone with surface area S=4 n that has the largest volume?

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The volume of a right circular cylinder of radius X and height y is given by V= TtX¯y, Suppose that…

Q: The volume of a right circular cone of radius x and height y is given by V = ¬Tx°y. Suppose that the…

A: Given: V = 216π cm3

Q: (d) A sphere of radius 0.4 m and having negligible weight is floating in a large freshwater lake.…

A: Given: The sphere of radius 0.4 m. The density of water is 1000 kg/m3. Calculation: Suppose the…

Q: The surface area of a sphere increases at a rate of 84 m2/sec. Then the rate at which the radius…

Q: A copper wire in 4 mm in diameter is evently wound about a cylinder whose length is 24 cm and…

Q: The base of solid is given by 9x² +4y = 36 on the xy-plane. The cross section is a square that is…

A: Let A(x) denote the cross-section area in a plane perpendicular to the x-axis, where a≤x≤b. Then,…

Q: The surface area of a sphere increases at a rate of 57 m2/sec. Then the rate at which the radius…

A: Let r is the radius of the sphere . S is the surface area of the sphere. we know that…

Q: The surface area of a sphere increases at a rate of 82 m2/sec. Then the rate at which the radius…

Q: A circular swimming pool full of water has a diameter of 24 ft and the sides are 5 ft high. Set-up…

Q: Find the volume of the washer that is obtained when the shaded area is rotated about the x-axis. ry…

A: Given that y=x+2,y=2 The formula for washer method is, V=π∫abf(x)2-g(x)2dx Here in the problem,…

Q: Derive the equation for the volume of a sphere of radius r using the shell method.

A: Consider a circle of radius (r), which when rotated around x-axis generates a sphere.

Q: A cylindrical tank of radius 5 ft and height 9 ft is two-thirds filled with a liquid of weight…

A: Solution

Q: 5. Consider a hollow spherical bowl with radius r = 18 cm that is filled to the top with water. h(t)…

Q: The surface area of a sphere increases at a rate of 77 m2/ sec. Then the rate at which the radius…

Q: 5. For the right circular cylinder, suppose that r = 5 in. and h = 6 in. Find the exact and…

Q: A circular swimming pool full of water has a diameter of 24 ft and the sides are 5 ft high. Set-up…

Q: The radius of a spherical ball is measured at r = 25 cm. Estimate the maximum error in the volume…

Q: The surface area of a sphere increases at a rate of 95 m2/ sec. Then the rate at which the radius…

Q: The surface area of a sphere increases at a rate of 82 m² / sec. Then the rate at which the radius…

A: Use rate of change

Q: 1. Find the volume of the solid that results when the shaded region is revolved around the Y - AXIS.…

Q: What is the radius (r) and height (h) of a cylindrical can holding 1L of oil that minimizes the cost…

A: 5

Q: Find the dimensions of the open cylindrical tank where the volume inside is maximized and that the…

A: Let r, h be the radius of the cylindrical tank. Now, Let S represent the Surface area of the open…

Q: A Cylindrical tank below with radius(R) and hight (H) have two holes ,one at the side at distance…

A: we have given a cylinderical tank with radius R and height H , two holes one at side at distance a…

Question

Suppose a cylindrical can is being made to hold 1 liter of oil. Design the can so
that the minimum amount of metal can be used. The area of the metal is given by
1000
A=27r27 rh Note that 1L = 1000cc so zr h
1000, h
2

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

Trending now

This is a popular solution!

Step by step

Solved in 4 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

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.
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.
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.
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. Compute the base area of a right circular cone that is 15.8 centimeters high and has a volume of 1070 cubic centimeters.
Determine whether the statement is true or false. a A right circular cone has exactly two bases. b The lateral area L of a right circular cylinder with radius length r and height h is given by L=2rh.
Solve these prism and cylinder exercises. Where necessary, round the answers to 2 decimal places unless otherwise specified. The frustum of a right circular cone has a larger base area of 40.0 square centimeters and a smaller base area of 19.0 square centimeters. The height is 22.0 centimeters. Find the volume. Round the answer to the nearest cubic centimeter.