A can buoy is to be made of three pieces, namely, a cylinder and two equal cones, the altitude of each cone being equal to the altitude of the cylinder. For a given area of surface, what shape will have the greatest volume?

A can buoy is to be made of three pieces, namely, a cylinder and two equal cones, the altitude of each cone being equal to the altitude of the cylinder. For a given area of surface, what shape will have the greatest 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.CR: Review Exercises

Problem 2CR: The base of a right prism is a triangle whose sides measure 7cm, 8cm and 12cm. The altitude of the...

See similar textbooks

Related questions

Q: The volumes of two spheres are in the ratio 64:27. The ratio of their surface areas will be?

A: Volume of sphere =43πr3Surface area of sphere =4πr2

Q: Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A…

Q: FInd the diemsions of a rectangular box, open at the top, having volume 727cm^3, and requiring the…

A: Let the length, breadth and height of the box be denoted by a, b and h respectively, thenV=a × b × h…

Q: The lengths of the legs of a right triangle are 4 cm and 6 cm. If the triangle is rotated about one…

A: *to find : greatest volume of cone. *concept : for getting max volume we need to revolve triangle…

Q: The volume of a right cone is 23257 units³ If its radius measures 15 units, find its height.

A: We know that volume of a right circular cone of radius 'r' and height 'h' is given by formula in…

Q: The diameter of a cylindrical construction pipe is 4 ft. If the pipe is 23ft long, what is its…

A: Radius of pipe = diameter/2

Q: The sum of the lengths of all edges of a cube is 60 cm. Find the volume V and the surface area T of…

A: Given: The sum of the lengths of all edges of a cube is 60 cm. The number of edges in a cube is…

Q: Two similar pyramids have lateral areas 8 ft 2 and 18 ft 2 If the volume of the smaller pyramid is…

A: If we let "s" be the length of a side in the smaller pyramid and "S" be a length of a corresponding…

Q: A cube has an edge of length 30. A rectangular solid has edge of lengths 20, 30 and L. If the cube…

A: Given: A cube has an edge of length 30. A rectangular solid has an edge of lengths 20, 30 and L.…

Q: Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A…

A: We find volume of both containers then find percentage

Q: If you fit the largest possible cone inside a sphere, what fraction of the volume of the sphere is…

A: In the given question we have to tell about the fraction of the volume of the sphere occupied by the…

Q: When would one use method of washers rather than the method of disks to find volume of solids?

A: When would one use method of washer rather than disks method:

Q: 4. The altitude of a right hexagonal prism is twice as long as the edge of the base. If the prism…

A: Given Volume = 1923in3

Q: If the diameter of the base remains constant, by what factor should the altitude be multiplied to…

Q: A steel storage tank for propane gas is to be constructed in the shape of a right circular cylinder…

A: Given, A steel storage tank for propane tank gas is to be constructed in the shape of a right…

Q: The box with dimensions indicated is to be constructed of materials that cost 1 cent per square inch…

A: Given- Material that cost for lateral surface area is 1 cent per square inch and for base it is 2…

Q: A cylinder has a volume of 78cm. What is the volume of a cone with the same radius and height?

Q: The volume of a circular cylinder is 1280A m³, and its height is 5 m. What is the radius of its…

Q: The base of a right prism is a rhombus one side of which is 10 cm, and the shorter diagonal is 12…

A: We will find the volume of the right angle prism in the following step.

Q: Find the dimensions of a rectangular prism whose volume is (x4 ‒ y4) units3.

A: Given that, volume, v = (x4 ‒ y4) units3

Q: the length of a side of a cube is equal to the radius of a sphere. which solid has the greater…

A: The length of a side of a cube is equal to the radius of a sphere. Let x be the side of a cube, then…

Q: A cone and a cylinder each have radius of 3 and height 4 - ratio of 3:4. what is the ratio of their…

A: given, A cone whose radius=3 and height =4A cylinder whose radius=3 and height =4

Q: The portable building shown below has straight sides that are 2 meters high, a diameter of 6 meters,…

A: Given a portable building which is in the form of cylinder surmounted by a cone. Dimensions of the…

Q: According to Cavalieri's Principle, which pair of shapes would have equal volumes?

A: the volume of the cone, pyramid , cylinder , sphere , rectangular prism , are given by volume of…

Q: A sphere is inscribed in a right circular cone whose slant height has a length equal to the diameter…

A: Given: A sphere is inscribed in a cone whose slant height equal to diameter =12 cm

Q: A margarine tub has the shape of the frustrum of a cone. With the lower base having diameter length…

A: Volume of frustrum of the cone is, V=13πR2H-r2h ...(1)

Q: If a cone has a radius of 5 and a height of 12. What is it’s volume ?

A: Given radius of cone(r)=5Height of cone (h)=12We know that volume of cone is πr2h3

Q: In a hollow cylinder, the sum of the external and internal radii is 14 cm and the width is 4 cm. If…

A: Given that, the sum of the external and internal radii is 14 cm and the width is 4 cm. The height of…

Q: If the radius length of one sphere is three times as long as the radius length of another sphere,…

A: Let a be the length of the radius of the smaller sphere.Since, it is given that the length of one…

Q: If a closed tin can of volume 16? in3 is to be in the form of a right-circular cylinder, find the…

A: Consider the provided question, In your question given, If a closed tin can of volume 16? in3 to be…

Q: The radius of a cylinder is multiplied by 9 while the height is kept the same. What effect does this…

A: We have to find volume of cone

Q: When the radius of a sphere is doubled, the volume of the new sphere is as large as the volume of…

A: The new radius is 2r now, So, the new volume will be: V=43π(2r)3=43π(8r3)=843πr3=8(old volume)

Q: An oil refinery is located on the north bank of a straight river that is 2 km wide land to a point P…

A: Refinery located on north bank cost $200,000/km over the land at point P on north bank to construct…

Q: A pressure tank has a hemispherical base surmounted by a right circular cylinder and which in turn…

A: we know that volume of semi sphereV1, volume of right circular coneV2 and volume of cylinder V3 is…

Q: The lateral edge of a square prism is 20cm long and it is inclined at an angle of 60 degrees with…

Q: One sphere has a diameter of 10 cm, and another sphere has a diameter of 4 cm. What is the…

A: Volume of sphere= (4/3)πr³ Where r is the radius of sphere Given diameter of ist Sphere, D1 = 10…

Q: A cylindrical can containing pieces of fruit is filled to the top with syrup before being sealed.…

A: Given that area of the base of the cylindrical can is 75 cm² and the height of the can is 10 cm. 110…

Q: The volumes of two similar rectangular solids are 1000 cm3 and 64 cm3. What is the ratio of their…

Q: A sphere is cut by two parallel planes 3 cm apart, in such a way that the radius of the upper…

A: Given , A sphere is cut by two parallel planes 3 cm apart, in such a way that the radius of the…

Q: has dimensions of 9 in., 10 in., and I ft. 21. Find the volume and the surface area of a "closed…

A: Solution Formula Volume =(length × breadth × height) Surface area =2(lb+lh+hb)

Q: The volume of a right circular cone is 36 t. If its altitude is 3, find its radius.

Q: The edge of a regular dodecahedron is 6 m, what is its total surface area?

A: Given: The edge of a regular dodecahedron is 6 m. To Find: Total surface area of the given regular…

Q: A dog trainer has 66 ft of fencing with which to create a rectangular work area for dogs. If the…

A: Given:Perimeter = 66 ftArea = 182 ft2

Q: The bases of a right prism is a hexagon with one of each side equal to 8 cm. The bases are 15 cm…

Q: Two similar cones have volumes 12π and 96π. If the lateral area of the smaller cone is 15π, what is…

A: since the cones are similar so l1l2 = r1r2 the the volumes are v1=12π unit3 , v2=96π unit3 so curved…

Q: Find the volume of the cone given its radius is 4 cm and its slant height of 6 cm. If necessary,…

A: Given query is to find the volume of the cone.

Q: A square pyramid and a triangular pyramid each have a base that measures 36 square inches. The…

A: To find the relation between heights of pyramids

Q: A regular square pyramid has lateral area of 60m^2 and base edge of 6m. What is its volume?

A: Given that, A regular square pyramid has lateral area of 60 m2 and base edge of 6 m. We have to find…

Question

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 3 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Triple Integral$

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

If the radius length of one sphere is three times as long as the radius length of another sphere, how do the surface areas of the spheres compare? How do the volume compare?
Kristine creates an open box by cutting congruent squares from the four corners of a square piece of cardboard that has a length of 24 in. per side. If the congruent squares that are removed have sides that measure 6 in. each, what is the volume of the box formed by folding and sealing the flaps?
The numerical value of the volume of a cube equals the numerical value of its total surface area. What is the length of each edge of the cube?
As in Exercise 39, find the volume of the box if four congruent squares with sides of length 6 in. are cut from the corners of a rectangular piece of poster board that is 20 in. wide by 30 in. long. Kristine creates an open box by cutting congruent squares from the four corners of a square piece of cardboard that has a length of 24 in. per side. If the congruent squares that are removed have sides that measure 6 in. each, what is the volume of the box formed by folding and sealing the flaps?
A cylindrical storage tank has a depth of 5 ft and a radius measuring 2 ft. If each cubic foot can hold 7.5 gal of gasoline, what is the total storage capacity of the tank measured in gallons?
For the right triangular prism, suppose that the sides of the triangular base measure 4 m, 5 m, and 6 m. The altitude is 7 m. a Find the lateral area of the prism. b Find the total area of the prism. c Find the volume of the prism.
If the tank in Exercises 41 needs to be painted and 1 pint of paint covers 50ft2, how many pints are needed to paint the exterior of the storage tank? A cylindrical storage tank has a depth of 5 ft and a radius measuring 2 ft. If each cubic foot can hold 7.5 gallon of gasoline, what is the total storage capacity of the tank measured in gallons?
The base of a right prism is a triangle whose sides measure 7cm, 8cm and 12cm. The altitude of the prism measures 11cm.calculate the lateral area of the right prism.
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?
Find the volume and the surface area of a closed box that has dimensions of 9 in., 10 in., and 1 ft.
The base of a right prism is a regular hexagon whose sides are 8cm in length. The height of the prism is 13 cm. Find the a Lateral area b total area c volume.