Consider a right circular cone of height 100. Find the average distance between a point inside the cone to the base of the cone

Q: Find the change in the lateral surface area of a right circular cone, with radius of base fixed as…

A: There is a right circular cone with base radius r and altitude height h.

Q: 17) If a right circular cone has a circular base with a diameter of length 10 cm and a volume of 50…

A: The diameter of circular base of the right circular cone is 10 m and so radius of circular base of…

Q: A cylindrical can with a height of 6 inches and radius of 1 inch is filled with a solid rectangular…

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Q: A right circular cylinder is inscribed in a sphere of radius 6 inches. Find the largest possible…

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Q: What is the spherical excess of a 600 cu cm spherical pyramid extracted from a sphere of radius 10…

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Q: Use cylindrical shells to find the volume

A: Given,       y=ex2, x=1, x=2, y=0, and revolved about the y-axis

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 surface area of a sphere of radius .

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Q: What is the area of the curved surface of a right circular cone of radius 3 and height 4?

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Q: Find the change in the lateral surface area of a right circular cone, with radius of base fixed as…

A: The lateral Surface area of a right circular cone is given as A =πrh2+r2        A2 =π2r2(h2+r2)…

Q: Find the area of lateral surface of a frustum of cone with altitude 4m. Radius of upper and lower…

A: Explanation: Here in the given question, we have a height/Altitude of a frustum of cone = 4m The…

Q: A sphere has a radius of 5.81 in., with a possible error of ± 0.003 in. Estimate the maximum error…

A: For a sphere of radius r the expression for the volume is V=43πr3. The error in r is denoted as ∆r.…

Q: Compute the surface area formed by rotating the portion of the curve in the first quadrant about the…

A: Given curve is x=(cost)(1+cost),y=(sint)(1+cost) , 0≤t≤2π Differentiate with respect to t.…

Q: A cylindrical tank that is 8 meters deep is half full of water and has a radius of 2 meters. Find…

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Q: Find the center of mass of a circular cone of regular steel of height (b)

A: It is given that a circular cone with height b and radius R

Q: Find the volume of the largest right circular cone that can be inserted in a sphere of radius 3.

A: The volume of the cone is given by  , where is the radius of the circular base of the cone and h is…

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: This container is composed of a right circular cylinder and a right circular cone. Which is closest…

A: Diameter d= 24 ftRadius r = 242ft    ⇒r = 12 ftheight of cylindrical part h = 10 ftlateral height l…

Q: Find the average distance of a point in a disk of radius a to a fixed point on the boundary of the…

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

A: Here we find the dimensions of cone.

Q: The line segment from (0,0) to (5,20) is revolved about the x-axis to form a cone. What is the…

A: First find equation of line then Use formula of volume

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: 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: What is the area of the curved surface of a right circular cone of radius 11 and height 60?

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: Find the circular cylinder of largest lateral area which can be inscribed in a sphere of radius 4…

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Q: If a right circular cone has a circular base with a diameter of length 10 cm and a volume of 100…

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Q: The factory designers are currently investigating whether a cone-shaped container can be replaced…

A: let the height of cone is h1  So , A/c the radius of cylinder and cone is same let 'r' and surface…

Q: Two solid spheres have radii of 4 cm and 6 cm respectively. They are melted and recast into a single…

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Q: A solid metal cylinder with radius 2 and height 2 is recast as a solid conewith radius 2. Find the…

A: Solution: Consider the given radius of the cylinder is r= 2 and height h = 2  Now if we recast it as…

Q: A right circular cone has a slant height of 12 ft and a lateral area of 96™ ft². Find its volume.

A: Let r be the length of radius of base, h be the altitude of the circular coneand l be the length of…

Q: Find the volume of the largest right circular cone that can be inscribed in a sphere of radius 3.

A: Cone: The volume of right circular cone V=13πr2h Where r is the radius of the circular base of the…

Q: Consider a right circular cone of height 100. Find the average distance between a point inside the…

A: Consider the equation of cone isz=x2+y2 and height of the cone is 100.To find:The average distance…

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

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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: Calculate the lateral surface area of a hollow lampshade shaped as a frustum of a cone. The lower…

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Q: What is the total surface area of a right circular cone of height 14 cm and base radius 2 cm?

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

A: Given data - Radius of sphere = 8 in. The right circular cone circumscribed about a sphere . We have…

Q: A cylindrical top hat has a radius of 11 centimeters and a height of 22 centimeters. What is the…

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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: Find the volume of the torus obtained by revolving the circle x^2 + y^2 = 4 about the line x = 3.

A: Find the volume of the torus obtained by revolving the circle x^2 + y^2 = 4 about the line x = 3.

Q: A right circular cylinder is inscribed in a sphere of radius 3 inches. Find the largest possible…

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Q: A cone is formed from a circular piece of material of radius 1 meter by removing a section of angle…

A: To determine the largest possible volume for the cone, if a cone is formed from a circular piece of…

Q: What is the surface area of this cylinder

A: surface area of cylinder =A r=radius = 3 in h = height =10 in

Q: Find the radius and height of the open right circular cylinder of largest surface area that can be…

A: Given, Open Right circular cylinder Sphere

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

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Q: Find the average distance from a point in a ball of radius to its center.

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Q: A right-circular cylinder is to be inscribed in a sphere of given radius. Find the ratio of the…

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Q: If a right circular cone has a circular base with a diameter of length 10 cm and a volume of 100T…

A: Given that, Diameter of right circular cone d = 10 cm So radius of right circular cone r = 5 cm And…

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.

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.