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

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

A: Given

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

A:

Q: Calculate the volume of the solid that is limited superiorly by the sphere x2+y2+z2=9 and inferiorly…

A: To Calculate: Volume of the solid bounded superiorly by x2+y2+z2=9 and inferiorly by x2+y2=z2.

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

A: Draw the region and use the washer method of finding the volume of revolution of solids.

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

A:

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

A:

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 whose base is bounded by the circle x2 + y2 = 16 and whose cross…

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Q: Find the volume of the solid whose base is a triangle with vertices (0, 0), (0, 5), and (5, 0).…

A: Sketch the base of the solid as follows.

Q: Determine the right circular cone of maximum volume that can be inscribed inside a given sphere of…

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

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

A:

Q: Consider a rectangular box B that has a bottom and sides but no top and has minimal surface area…

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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: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs…

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Q: (c) Semicircles (d) Isosceles right triangles y 2)

A: Part C) To find the volume of the solid whose bases are bounded by the circle x2+y2=4,  And the…

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

A:

Q: Find the volume in the first octant bounded by the cone z2 = x2 − y2 and the plane x = 4.

A: The given conic curve is, z2=x2-y2 Boundary limits are as follows, Limit of x: 0 to 4Limit of y: 0…

Q: Find the volume of the solid whose base is a triangle with vertices (0, 0), (0, 4), and (2, 0).…

A: Given vertices of the triangular base is 0,0, 0,4 and 2,0. We know the equation of the line passing…

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

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

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Q: Find the volume generated by revolving the plane area generated by the equations y = ex^2, y=0, and…

A: To find the volume of solid formed when the region bounded by y=e-x2, y=0 and  x=0  about the…

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

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Q: Use cylinder shell method to graph and find volume: y=sqrt(x), y=0, x=1, about x=-1

A: If a region is bounded by a curve y=fx and x-axis on the interval a,b and it is rotating about a…

Q: find the volume,The region bounded in back by the plane x = 0, on the front and sides by the…

A: Given

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

A:

Q: The axes of two circular cylinders of radius a intersect at right angles. Show that the volume…

A: 8∫0ady∫0a2-y2dx∫0a2-y2dz = 8∫0ady∫0a2-y2dx (a2-y2)8∫0ady∫0a2-y2dx∫0a2-y2dz  =8∫0ady…

Q: A right cylinder of radius r is inscribed in a hollow sphere of fixed radius a. The

A: Given, a right cylinder of radius 'r', is inscribed in a hollow sphere of fixed radius 'a'. The…

Q: Find the volume of the solid of revolution bounded by the circle +y = 16, and the lines 0 and

A: To find: Volume of the solid

Q: Find the center of mass of a thin plate of constant density & covering the given Region enclosed by…

A: Curve 1: y=x-x2 Curve 2: y=-x We have to find the center of mass.

Q: FiNd the volumes OF the solids gewerated by revolving +he regions bounded by the graphs oF the…

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

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Q: Find the volume of the largest right circular cylinder that can be inscribed in a sphere of radius…

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

A:

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 mass of a circular cone of height b and radius of base a whose density varies as the…

A: To find: The mass of a circular cone. Given information: The height of the cone is b and base is a…

Q: he volume bounded by y = x², y = 0 and x = 2 rotated about the specified = specified orientation of…

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Q: Find the volumes of the solids generated by revolving the region in the first quadrant bounded by…

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

A:

Q: A cone of height H with a base of radius r is cut by a plane parallel to and h units above the base,…

A:

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.