A right circular cylinder is inscribed in a sphere of radius r. Find the largest possiblesurface area of such a cylinder.

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

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

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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 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: Assume that a cell is a sphere with radius `10^{-3}`  or 0.001 centimeter, and that a cell’s density…

A: given: a cell is a sphere with radius or 0.001 centimeter and a cell’s density is 1.1 grams per…

Q: A ball of radius 11 has a round hole of radius 5 drilled through its center Find the volume of the…

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Q: Show that a closed right circular cylinder of given surface has maximum volume if its height equals…

A: Let, the surface area be S, radius be r, height be h and volume be V. The total surface area be…

Q: Calculate the surface area of a sphere of radius a.

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Q: find the centroid of volume if the volum is equal to 7/15 π

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Q: Two identical spheres are placed so that one is on top of the other inside a right circular cylinder…

A: This question is related to cylinders and spheres, we will solve it using given information.

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

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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: Use the Theorem of Pappus to find the exact volume of a general cone created vertices (0, 0), (1,0),…

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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: Find the volume enclosed by the cy linder (x-1) ty²=1 and the sphere x² +y²7z²=L4.

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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: A solid has a circular base of radius 3. What is the volume of the solid if vertical cross-sections…

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Q: Consider a right-circular cylinder of diameter 1. Form a wedge by making one slice parallel to the…

A: The diameter of the right circular cylinder is d=1. The angle which is made by other slide to the…

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: Suppose that a semicircular region with a vertical diameter of length 4 is rotated about that…

A: Given: A semicircular region with a vertical diameter of length 4 is rotated about the diameter. To…

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

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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 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: Show that the rectangular box (including the top and bottom) withfixed volume V = 27 m3 and smallest…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

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: Find the volume of the largest right circular cone that can be incribed in a sphere of radius 3. 3 y…

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Q: A cone with a circular base of radius 6 cm is to be made so that the distance from the apex of the…

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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 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 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: A right prism has height h and bases that are regular hexagons with sides s. Show that the volume is…

A: It is given that bases are regular hexagons with sides 's'. It clear from the figure that a hexagon…

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

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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: Show that the surface area of a closed cuboid with square base and given volume is minimum , when it…

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Q: A sphere with radius r is inscribed in a cylinder. Find the volumeof the cylinder in terms of r.

A: let a right circular cylinder of radius 'R' and height 'H' is inscribed in the sphere of the given…

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 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: Find the volume of the cap of a sphere with radius R and height h using a triple integral. R.

A: Consider the following figure By Pythagorean theorem x2+y2=R2 ⇒x2=R2−y2

Q: Two identical spheres are placed so that one is on top of the other inside a right circular cylinder…

A: topic - volume of cylinder

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: 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 ball of radius 12 has a round hole of radius 5 drilled through its center. Find the volume of the…

A: let the resulting volume of solid is Vr  Vr = 6452.83 detailed solution is given below

Q: Show that the surface area of a closed cuboid with square base and given volume is minimum, when it…

A: Let the length be x , breadth be x and height be y of a closed cuboid with a square base.So Volume…

Q: Find the volume generated by y = x^2, x=0 and y = 4 rotated about the y axis. with drawing please.

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