A right traingle of a given hypotenuse is rotated about one of its legs to generate a right circular cone. Find the cone with the greatest volume.

Q: Determine the volume if the area common with y²-3x+7y=8 and x²-4x+3=y² is revolved about the…

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Q: Use the Theorem of Pappus to find the volume of thegiven solid.52. A sphere of radius r

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Q: Find the exact volume of the solid of revolution that results when a semicircular region with…

A: We know that if as semicircle is rotated about diameter then resulted figure will be sphere, whose…

Q: A solid dome is to be constructed with the ellipse x^2+3y^2=6 as a base. Using infinitely many…

A: Given that the solid dome is to be constructed with the ellipse x2+3y2=6 as a base. We have to…

Q: Calculate the volume of one of the wedge-like objects formed by cutting the cylinder x²+9y²=a² with…

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Q: a) Find the volume and the lateral surface area of the solid formed by rotating this func- tion…

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Q: Find the volume of the ellipsoid =D1 in positive octant Once

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Q: Find the volume of the solid whose base is given by 9. whose cross-sections perpendicular to the…

A: We will first find the area of cross section. Then integration of Area will be required volume of…

Q: A right-circular cone is to be circumscribed about a sphere of given radius. Find the ratio of the…

A: Let R be the radius of the cone, l its slant height and h be the height. V= 13πR2h We have to make…

Q: Find the volume of the solid whose base is the semicircle y = √9 - x² where -3 ≤ x ≤ 3, and the…

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Q: Find the volume of the solid cut from the thick-walled cylinder 1 ≤ x2 + y2 ≤ 2 by the cones z =…

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Q: Use the Theorem of Pappus to find the volume of thegiven solid.A cone with height h and base radius…

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Q: Calculate the volume generated by the circle x^2 + y^2 -4x=-3 that revolves around ox

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Q: Find the volume of the smaller wedge cut from a sphere of radius 10 by two planes that intersect…

A: Here we have to find the volume of the similar wedge cut from a sphere of radius 10 by two planes…

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: Use the Theorem of Pappus to find the exact volume of a general cone created by rotating a triangle…

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Q: A rectangle has dimensions of 6 in. by 3 in. Find the exact volume of the solid of revolution formed…

A: Given that, Rectangle with Dimensions of 6 in by 3 in.   If we rotate this rectangle then it forms…

Q: If the shape below is rotated around the y-axis, what is the volume of the resulting shape? Round to…

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Q: Determine the volume if the area common with y^2-3x+7y=8 and x^2-4x+3=y^2 is revolved about the…

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Q: Find the Volume enclosed by N = x2+y² and

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Q: Find the volume of a stereoscopic body by rotating a given straight line around an axis surrounded…

A: As per our guidelines, we are allowed to answer only one question. Since you have asked multiple…

Q: A solid dome is to be constructed with the ellipse x^2+3y^2=6 as a base. Using infinitely many…

A: Graph the ellipse.

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: A square pyramid whose base width is óm has an altitude of 12m is cut by a plane parallel to the…

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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: Solve for the radius of a right circular cone of maximum volume which can be inscribed in a sphere…

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Q: Find the volume of the largest circular cone that can beinscribed in a sphere of radius r.

A: Let the largest circular cone that can be inscribed in a sphere of radius r as shown below: OC=OA=…

Q: Does Cavalieri's Principle apply to the volumes of the cones shown? Explain. The cones have and The…

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Q: A cylindrical drill with radius 1 is used to bore a hole through the center of a sphere of radius 5.…

A: To Determine: A cylindrical drill with radius 1 is used to bore a hole through the center of a…

Q: A rectangular box with a square base is inscribed in a right circular cone of height 4 and base…

A: Given:A rectangular box with a square base is inscribed in a right circular cone.The base radius of…

Q: Find the volume of a right spherical segment of 2 bases if the radius of the sphere is 10 in.; the…

A: To find the volume of a right spherical segment of 2 bases. If the radius of the sphere is 10…

Q: The base of a solid circular with a radius of 4 cm. Determine its volume if every plane…

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Q: Find the volume enclosed by the torusp = 4 sin().-

A: The volume is given by: V=∫∫∫dv In spherical co-ordinate dV=ρ2sin φ dρ dφ dθ

Q: 2Ay-3-2r

A: In this question we find volume of the shaded region that is revolved arround y-axis.     Here i…

Q: rated by revolving the area bounded by the parabola y² = 8x and its latus rectum about the latus…

A: Introduction: The chord that passes across the focus of a parabola and is perpendicular to the…

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

A: Volume of the cone is given by 13πr2h, here r is the radius of cone (and not the sphere), h is…

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

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Q: Q1: Aolid carton made from a 2700 cm' of paperboard, as shown in the figure. If the carton is…

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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: Find the volume generated by revolving the area bounded by the parabola x2 = 4y and its latus rectum…

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Q: Find the volume rotated about the x-axis

A: Formula

Q: Find the exact volume of the solid of revolution that results when a rectangular region with…

A: Given data: When the rectangle is rotated about its length then the revolution gives the right…

Q: Q1: A solid carton made from a 2700 cm' of paperboard, as shown in the figure. If the carton is…

A: Prepare the problem as given: Volume covered: f(x,h) = hx2 Restrain: g(x,h) = x2+4hx = 2700 need to…

Q: Engr Thomas Pendot wants to construct a frustum from a right circular cone. At what distance from…

A: Let h be the distance from the base of the right circular cone which also the height of the frustum.…

Q: Find the dimensions of the closed right circular cylindrical can of smallest surface area whose…

A: According to the given information it is required to find the dimension of right circular cylinder…

Q: Find the volume of the portion of the solid sphere ps8 that lies between the cones o= and ф %3D 3 3…

A: The portion of the solid sphere ρ≤8 that lies in between the cones ϕ=π3  and  ϕ=2π3

Q: If we have a half-circle of radius r centered at 0, prove thatthe volume of the sphere resulting…

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Q: Determine the solution in finding the dimensions of the right circular cylinder, with the greatest…

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Q: Find the dimensions of the closed right circular cylindrical can of smallest surface area whose…

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Q: Find the volume of the solid whose base is the semicircle y = v9 – x2 where -3 < x < 3, and the…

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Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.