Answered: The altitude of a cylinder of maximum…

The altitude of a cylinder of maximum volume that can be inscribed in a right circular cone of radius r and height h is: h/3 3h/2 h/4 2h/3

Mathematics For Machine Technology

8th Edition

ISBN:9781337798310

Author:Peterson, John.

Publisher:Peterson, John.

Chapter65: Achievement Review—section Six

Section: Chapter Questions

Problem 51AR

See similar textbooks

Related questions

Q: Show by integration that the volume V of a right circular cylinder with base radius r and height h…

Q: 3. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus…

A: Given

Q: Rotate a circle of radius r around the x axis and use the method of disks to prove the formula for…

Q: Find the dimensions of the right circular cone of minimum volume V that can be circumscribed about a…

Q: Find the radius and height of a cylindrical can of total surface area A whose volume is as large as…

A: Find the radius and height of a cylindrical can of total surface area A whose volume is as large as…

Q: 2. The area of the parabola x2 = 4y – 4 cut through its latus rectum is revolved about the…

A: 2) Parabola; x2=4y-4End points of the latus rectum (-2,2) and (2,2)vertem = (σ 1)using washer method

Q: (1 point) The volume of the solid obtained by rotating the region enclosed by y = a², y = 2x, about…

A: y=x2y=2x about line x=2 for point of intersection x2=2xx2-2x=0x(x-2)=0x=0,2

Q: what is the volume generated if the area bounded by the cirves x2 =8y , x=4 and y= 0 is resolved…

Q: 3]. , Let V = ar²h, where V the volume of a right circular cone of radiusr and height h. Show that…

Q: Sketch the region enclosed by the curves and find its area. 1 x = 0, y = 1, y = e3 x = -, NOTE:…

Q: A metal plug has been designed using the intersection of the two cones z = √√x² + y² and √x² + y² +…

Q: y = 9x² and y = 0 = about x = -4

A: First we plot the graph of the region and axis of revolution.

Q: Find the volume of the solid generated by revolving the “triangular” region bounded by the x-axis,…

A: Given information:

Q: . THe area enclased by the loop of the curved y= x (x - 3)° is Find the volume generated . revolved…

A: Here 1st we will find points where loop is formed and then shade the region bounded , To form the…

Q: The area bounded by the parabolas y² = 4x and x² = 4y is revolved about the y-axis. Find the moment…

A: The given equation of the parabolas are, y2=4x and x2=4y.

Q: A right circular cone is circumscribed by a sphere of radius 1. Determine the height h and radius r…

Q: For each problem, use the method of cylindrical shells to find the volume of the solid that results…

Q: Derive the formula for the volume of a right circular cone of height h and radius r using an…

A: Given information:

Q: Find the volumes of the solids whose bases are bounded by the circle x^2+y^2=4, with the indicated…

A: Given, x2+y2=4 Part a: We have, x2+y2=4⇒y2=-x2+4⇒y=±4-x2 Now we find the area to use in finding the…

Q: 3. Find the volume of a sphere with radius r by integration.

Q: Find the dimensions of the right circular cylinder of maximum volume that can be inscribed in a…

Q: Find the volume of the solid whose base is bounded by the circle x2 + y2 = 9 and whose cross…

A: To find the volume of the solid whose base is bounded by the given circle and whose cross-sections…

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

Q: 2. Find the volume of a cylinder with a radius of r and height h by integration.

Q: 4. Find the radius of the right circular cone with least volume that can be circumscribed about the…

A: Formula Used: Volume of Cone = 13πR2h where R,h denote the radius and height of right circular…

Q: To find the volume of the solid generated by revolving the region bonded by x = 12(y² – y³) and the…

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: For a cylindrical can (depicted in the figure, height h and radius r) with volume 2π m³, compute the…

A: Surface area = 2πrh+2πr2 Volume =πr2h = 2π

Q: The area enclosed by y = 4x - x^2 and 2y = 2x + x^2 is revolved about the line x = -1. Using a…

Q: Find the dimensions of the right circular cone of the greatest lateral area that can be inscribed in…

Q: The region in the first quadrant bounded by x2 + y² = 1, x 2, and y = 1 is revolved about: 1- The…

Q: Find the volume generated by the area bounded by the y-axis, the line y=1, and the arc of y=sin x…

Q: Hence, calculate the volume of the solid bounded above by the surface z = sin(x³) and below by the…

A: Solution:

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the given…

A: Topic- volume by revolution

Q: 9. Find the demensions of the right circular cylinder of largest volume that can be inscribed in a…

Q: The volume of the solid obtained by rotating the region enclosed by 1 y = 0, x4 y = x = 3, and x =…

A: Plot the given curves y=1x4, y=0, x=3, x=6 on a co-ordinate plane and obtain the region enclosed by…

Q: Find the volume, if an area bounded by an asteroid I = cos t y = sin³ t ve y = -/I+x ,y-axis, and…

Q: Neyinder is inscribed in a right circular cone of height 2.5 and radius (at the base, equal to 3.…

Q: The altitude of a cylinder of maximum volume that can be inscribed in a right circular cone of…

A: We have to find Altitude

Q: 1. Show by integration that the volume V of a right circular cylinder with base radius r and height…

A: We’ll answer the first part of this question. since due to complexity. Please submit the question…

Q: Find the volume generated by revolving about the line x - 4 = 0 the area bounded by the curve x2 =…

Q: 2. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus…

Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the giveN…

A: Given: y=6-2x-x2 and y=x+6 about the x-axis. To find the volume of the solid bounded by the given…

Q: Find the center of mass of a thin plate of constant density δ covering the given regions. The…

Q: Right circular cones of height h and radius r are attached to each end of a right circular cylinder…

A: Let Vcr be the volume of the cone and Vc be the volume of the cylinder. So, Vcr=πr2h and Vc=13πr2h.

Q: A right traingle of a given hypotenuse is rotated about one of its legs to generate a right circular…

A: Using Pythagoras theorem and by application of derivative we can find the maximum volume.

Q: Consider a thin plate of constant density d lying in the regionbounded by the graphs of y = √x and x…

A: First find the intersection points of the given curve, by equating the y of both curves…

Question

The altitude of a cylinder of maximum volume that can be inscribed in a right circular cone of radius r and height h is:
A
h/3
3h/2
h/4
2h/3

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps with 2 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.
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.
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.
Find the exact volume of the solid that results when the region bounded in quadrant I by the axes and the lines x=9 and y=5 revolved about the a x-axis b y-axis
A solid is formed by cutting a conical section away from a right circular cylinder. If the radius measures 6 in. and the altitude measures 8 in., what is the volume of the resulting solid?