4. A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 20 cubic cm. Find the radius of the cylinder that produces the minimum surface area. h

4. A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 20 cubic cm. Find the radius of the cylinder that produces the minimum surface area. h

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: 13. Find the dimensions of the closed cylinder volume V=16 that has the least amount of surface…

Q: Show that a rectangular box of given volume and minimum surface area is a cube.

Q: We want to construct a box with a square base that has a volume of 100 cm^3 . Assuming that all the…

Q: 7. A manufacture want to design an open box having a square base and a volume of 256 cm³. What…

A: Given problem is :

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 container with circular base is to hold 64 in^3. Find its dimensions so that the…

Q: b. A container in the shape of a right circular cylinder with no top has a surface area of 15 ft?.…

A: We have to find the height and base radius for which the volume of the cylinder will be maximized.…

Q: 3. Determine the dimensions of the right circular cylinder, with the greatest volume, that can be…

Q: 1. A long metal sheet with a width of L meters is formed into a gutter by bending up two of its…

A: A roof gutter is to be made from a long strip of sheet metal L units wide, by bending up equal…

Q: Determine the dimensions of a rectangular box with a volume of 1 ft ^ 3 that has a minimum surface…

A: Given a rectangular box with volume 1 ft^3

Q: 7. Determine the dimensions of a rectangular box, open at the top, having a volume of 32 ft³, and…

Q: A frustum of a conical tank whose upper radius is 10 cm, lower radius of 8 cm and height of 12 cm is…

Q: Find the exact maximum and minimum volumes (in cm) of a rectangular box whose surface area is 1,300…

Q: A closed rectangular box has volume 26cm^3. What are the lengths of the edges giving the minimum…

A: Given a rectangular box which has volume 26 cm^3.

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

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: Show that the largest cylinder that could be inscribed in a sphere of radius 4Tr3 r has a volume of…

Q: Which has a bigger volume, a sphere with radius 2 meters or a pyramid with base 2.5 meters and…

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

Q: Prove mathematically that a cylinder with hemispherical ends that has the same volume as a sphere…

A: Let r be the radius of the hemispherical end. Let h be the height of the cylinder. Let r' be the…

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

A: Given: Volume V=60 ft3

Q: West Coast Customs is constructing a closed-top, square-based, rect- angular subwoofer box that will…

A: Here we use application of derivatives to find the minimum surface area and find it's dimensions.

Q: A cylinder with no top is to have a volume of 100π cubic centimeters. Find the minimum possible…

A: To find the minimum possible surface area of the given type of cylinder.

Q: 1. A closed cylinder of volume 600 cm³ is made using a metal sheet. Find the radius that will…

A: The formula to calculate the volume of the cylinder is V=πr2h. And the volume is given as 600 cm3.…

Q: A cylindrical can has a volume of 1024r cm. What dimensions yield the minimum surface area?

Q: Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm2 and whose…

A: Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm2 and whose…

Q: A closed rectangular box has volume 20 cm³. What are the lengths of the edges giving the minimum…

A: Solution is given below:

Q: 8.Show that the rectangular box of maximum volume with a given surface area is a cube

Q: 10. The minimum surface area for a given volume of a cylinder occurs when: *

A: The volume of the cylinder is V=πr2h therefore, h=Vπr2 the surface area of the cylinder is given by…

Q: 11. A telephone booth in the shape of a square-based prism is to have a volume of 832 m³. Determine…

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

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

Q: 7. Determine the dimensions of a rectangular box, open at the top, having a volume of 32 ft³, and…

A: Given :Volume = 32 ft3

Q: A company that manufactures dog food wishes to pack the food in closed cylindrical tins. What…

A: Given volume of the can is (128)πcm3 Let height=h radius=x

Q: A box, used to package men's shirts, is in the shape of a square-based prism and its to have a…

A: Given Data: The volume of the square-based prism is: V=8400 cm3 The equation of surface area is:…

Q: 13. Find the dimensions of the closed cylinder volume V=16n that has the least amount of surface…

A: Let the radius of the cylinder be: r Let the height of the cylinder be: h Therefore the volume of…

Q: 7. Determine the dimensions of a rectangular box, open at the top, havin volume of 32 ft3, and…

A: Given that the volume of the rectangular box is 32 ft3.

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

Q: 2.Find the volume of the largest circular cylinder that can be inscribed in a sphere of radius R

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

Q: A closed box with a square base is to be built and the volume fixed at 30 m3. Determine the minimum…

A: Let the square base has side as x and height is y then the volume of the square base cuboid is…

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

A: Introduction :

Q: A closed box with a square base is to be built and the volume fixed at 30 m3. Determine the minimum…

A: To find: The minimum cost of the box. Given: The cost of front and top is P1.5 and the bottom and…

Q: 6. Show that when a hole of radius a is bored through the center of the sphere of radius b, the…

A: Given: The radius of the sphere is b. The radius of the hole is a. We have to show that the volume…

Q: 1. Find the height of a circular cylinder of maximum volume, which can be inscribed in a sphere of…

Q: A poster is to contain 300 m^2 of printed matter with margins of 10 cm at the top and 5 cm at each…

Q: A rectangular tank with a square base, an open top, and a volume of 16,384 ft° is to be constructed…

A: Given : Volume of rectangular is given 16384 ft3 Now we find surface Area and dimensions

Q: 4. West Coast Customs is constructing and open-top, square-based, rect- angular subwoofer box that…

A: West Coast Customs is constructing and open-top, square-based.rectangular subwoofer box that will…

Question

Please show work

4. A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of
the solid is 20 cubic cm. Find the radius of the cylinder that produces the minimum surface area.

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 with 4 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

The surface of a soccer ball is composed of 12 regular pentagons and 20 regular hexagons. With each side of each regular polygon measuring 4.5 cm, the area of each regular pentagon is 34.9 cm2 and area of each regular hexagon is 52.5 cm2. a What is the surface area of the soccer ball? b If the material used to construct the ball costs 0.8 of a cent per square centimeter, what is the cost of the materials used in construction?
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.
Given that a regular polyhedron of n faces is inscribed in a sphere of radius length 6 in., find the maximum largest possible volume for the polyhedron.