Maximum-volume cylinder in a sphere Find the dimensions ofthe right circular cylinder of maximum volume that can be placedinside a sphere of radius R.

Q: The base of a solid is a circle with radius 4. Each cross section perpendicular to a fixed diameter…

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Q: A cone is constructed by cutting a sector from a circular sheet of metal with a radius 19. The cut…

A: A cone is constructed by cutting a sector from a circular sheet of metal with a radius 19. The cut…

Q: Optimal popcorn box A small popcorn box is created from a12" x 12" sheet of paperboard by first…

A: Height of box ⇒12-x2-x2⇒12-xLength ⇒6-xDepth ⇒xSo,V = (12-x)(6-x)(x)V = x3-18x2+72xfor max.…

Q: Time A solid is formed with a base that is a triangle with vertices at (0,0), (3, 0) and (0, 1).…

A: y-10-1=x-03-0  y-1=-x3y=1-x3

Q: An open box is to be made from a piece of cardboard that measures 18 by 24cm. Equal sized squares x…

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Q: Example: Suppose a box with no top is to hold a certain volume V. Find the dimensions for the box…

A: The maximum or minimum value of the function given the constraint can be calculated by using the…

Q: Find the maximum volume of a rectangular box that is inscribed in a sphere of radius r. Need Help?…

A: Let the sphere of radius r The diagonal of the rectangular box is twice the radius, that is 2r. Let…

Q: A hemisphere of radius 1 sits on a horizontal plane. A cylinder stands with its axis vertical,…

A: Given that a hemisphere of radius 1 sits on a horizontal plane

Q: 13. A right circular cylinder is inscribed inside a sphere with radius r = 3 inches. Find the…

A: The radius of the sphere is 3 inches.

Q: A right circular cylinder is inscribed in a sphere of radius 10 cm. Find the dimensions of the…

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

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

Q: A cylinder is inscribed in a right circular cone of height 6.5 and radius (at the base) equal to 4.…

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Q: A closed rectangular box with faces parallel to the coordinate planes has one bottom corner at the…

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Q: Maximum Volume Find the volume of the largest right circular cone that can be inscribed in a sphere…

A: Largest volume can be find by checking the sign of second derivative of volume. If the sign is…

Q: 9. A cylinder is inscribed in a sphere of radius a. Find the maximum volume.

A: As per our guideline we are allowed to answer only one question. Kindly repost the other question as…

Q: A box with an open top has vertical sides, a square bottom, and a volume of 4 cubic meters. If the…

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Q: Cylinder in a cone A right circular cylinder is placed inside acone of radius R and height H so that…

A: Given that: A Cylinder in a cone a right circular cylinder is placed inside acone of radius “R” and…

Q: The solid lies between planes perpendicular to the X - axis at x = -1 and x = 1. The cross -…

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Q: 1. A rectangle is bounded by the X-axis and the semicircle in the positive y-region (see figure).…

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Q: A rectangular solid with a square base has an area of 432 square meters. a) determine the…

A: Given A=432 square cmA=2x2+4xy⇒2x2+4xy=432⇒y=432-2x24xvolume…

Q: A rectangular solid with a square base has a surface area of 37.5 square centimeters. (Let w…

A: (a) From the given, the surface area of the rectangular solid with square base is 37.5 cm2. Let the…

Q: find the volumes of the solids generated byrevolving the regions about the given axes. If you think…

A: Consider the following graph:

Q: A pyramid 3 m high has a square base that is 3 m on a side. The cross-section of the pyra- mid…

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Q: A very high end paint company wants to construct a paint can in the shape of a cylinder to hold 1000…

A: given container shape is cylindrical  let radius of base is r and height be h  volume of container…

Q: Maximum Area Find the dimensions of the largest rectangle that can be inscribed in a semicircle of…

A: Largest rectangle

Q: 3. A container in the shape of a (right) cylindrical can with an open top of volume 87 cm³ is to be…

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Q: The base of a solid is a circle with radius 4. Each cross section perpendicular to a fixed diameter…

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Q: 4. A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The…

A: Volume of the cylinder , V=πR2h Volume of the hemisphere ,V=43πR3

Q: A rectangle is bounded by the x-axis and the semicircle in the positive y-region (see figure). Find…

A: We have to find the dimensions of the largest rectangle that can be inscribed in a semicircle of…

Q: Find the maximum volume (in cubic units) of a rectangular box that is inscribed in a sphere of…

A: Given: The maximum volume (in cubic units) of a rectangular box that is inscribed in a sphere of…

Q: 2. A right-circular cone is to be circumscribed about a sphere of given radius. Find the ratio of…

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Q: A rectangle is bounded by the x-axis and the semicircle in the positive y-region (see figure). Find…

A: Given:Assume that the center of the semicircle be (0,0).

Q: 3. From a thin piece of cardboard 14 in by 14 in, square corners are cut out so that the sides can…

A: This question can be solved using the concept of maxima and minima.

Q: a cone. Find the magnitude of such that the volume of the cone is a maximum.

A: Given: It is given that,"A sector with central angle θ is cut from a circle of radius R = 6 inches,…

Q: A solid has a base which is a circle of radius 22. The cross sections perpendicular to the y-axis…

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Q: A volcano fills the volume between the graphs a 1 , and outside the cylinder z2+y = 1. Find the…

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Q: A cylindrical package to be sent by a postal service can have a maximum combined length and girth…

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Q: 6. A water tank is shaped like a cone with the apex point at the bottom, where the cone has radius 5…

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Q: 7. Maximum Volume (a) Verify that each of the rectangular solids shown in the figure has a surface…

A: Simply I have applied the formula of cuboid and cube....go through the solution....you will get it…

Q: The plane region is revolved completely about the​ y-axis to sweep out a solid of revolution.…

A: We want to find the volume of revolution on  about the y-axis

Q: 3 volume? A cylinder is inscribed in a right circular cone of height 3 and radius (at the base)…

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Q: Examples: 1.) A curve wedge is cut from a cylinder of radius 3 by two planes. One plane is…

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Q: A right triangle whose hypotenuse is v11 m long is revolved about one of its legs to generate a…

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Q: A right circular cylinder is inscribed inside a sphere with radius r=3 inches. Find the maximum…

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Q: A cylinder is inscribed in a right circular cone of height 12 cm and base radius of 4 cm. Find the…

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Q: cylindrical shampoo container is to have volume 750 cm3 a) Determine the dimensions of the…

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Q: Maximum Volume A rectangular solid with a square base has a surface area of 337.5 square…

A: Part (a) -

Q: A rectangular box with an open top has a square bottom and a volume of 4 m³. Find the dimensions of…

A: Given that the volume of the rectangular box is 4 m3 and its bottom is a square.

Q: Cylinder in a cone A right circular cylinder is placed inside a cone of radius R and height H so…

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Q: Show! The Problem. A waterway in a theme park has a semicircular section with a diameter of 11 ft.…

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