The total amount of a cylinder inserted into a hemisphere of radius 1 unit What is the maximum value of the surface area?

Q: e radius of a right circular cone having a lateral area of 544.12 m² to have a maximum volume.

A: In this question, the concept of maxima and minima is applied. Maxima and Minima The critical points…

Q: 1. Sand is being poured into a conical pile in such a way that the height is always one-third of the…

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Q: A cylinder is inscribed in a right circular cone of height 6.5 and radius (at the base) equal to 3.…

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Q: A cylinder is inscribed in a sphere with radius 5. Find the height h of the cylinder with the…

A: Our aim is to inscribe a right circular cylinder inside a sphere with radius 5 cm such that the…

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Q: A trapezoidal section trough is formed by bending the edges of a sheet made of aluminum 15…

A: Let x be the length of edge bent which makes an angle of θ with the horizontal as shown in figure.…

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Q: A rectangular box with a square base and of top must have a volume of 32 cm°. Fiind the smalles…

A: Given that: A rectangular box with square base has volume of 32 cm3.

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

A: Since, a solid is formed by adjoining two hemispheres to the ends of a right circular…

Q: A coat of paint of thickness 0.5 mm is applied evenly to the surface of a sphere a radius 20 cm.…

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

A: Given, radius(r) and height(h) of cone

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: 7. A can (right circular cylinder) is to be made from 100 in of metal. What are the dimensions…

A: Given surface area is 100in2

Q: A vessel in the shape of a cone has a height of 48 cm and a base diameter of 16 cm. It holds water…

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Q: A tank, shaped like a cone has height.10 meters and base radius 3 meters long. It is placed so that…

A: We have to find work done  to pull out all water from tank.

Q: a cylinder is inscribed in a sphere of radius a,solve for the maximum volume.complete solution.

A: Given problem:- A cylinder is inscribed in a sphere of radius a,solve for the maximum volume

Q: A plane intersects a sphere with a volume of about 44.6 cubic meters through the center of the…

A: given data Volume of the sphere = 44.6 m³ find The area of the cross section Let "r" be the radius…

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

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

Q: A tank, shaped like a cone has height 10 meters and base radius 3 meters long. It is placed so that…

A: please refer to the image below

Q: A projectile is launched upward with a velocity of 160 feet per second from the top of a 95-foot…

A: given  u=160 ft/sec and h(0)=95

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 cylinder is inscribed in a right circular cone of height 5 and radius (at the base) equal to 5.5.…

A: Let the height of the cylinder is h and radius is r. The cylinder in inscribed in the cone of height…

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: Find the dimensions and volume of the right circular cylinder of maximum volume inscribed in a…

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Q: A vessel in the shape of a cone has a height of 48 cm and a base diameter of 16 cm. It holds water…

A: Given,  Height of cone= 48 cm Base diameter = 16 cm Radius of cone = 8 cm  Depth of water = 18 cm…

Q: A tank in the shape of an inverted right circular cone has height 9 meters and radius 19 meters. It…

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Q: A hemispherical tank of radius 2 feet is positioned so that its base is circular. How much work is…

A: Given -   Hemisphere tank of radius-2 feet  Hemisphere base is circular  weight density of water…

Q: A cylinder is inscribed in a right circular cone of height 7.5 and radius (at the base) equal to 8.…

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Q: A closed tank is made from a thin uniform metal. The tank is in the shape of a circular cylinder…

A: We know that lateral surface area of a cylinder is 2πrh, area of flat bottom is πr2, area of the…

Q: Acylinder is inscribed in a right circular cone of height 4.5 and radius (at the base) equal to 2.…

A: Let 'r' and 'h' be the radius and height of the cylinder inscribed inside the right circular cone.…

Q: A cylinder is inscribed in a right circular cone of height 2.5 and radius (at the base) equal to 5.…

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Q: A storage unit has the shape of a hemisphere on top of a cylinder and a fixed volume V (Figure 10a).…

A: It is given that a storage unit has the shape of hemisphere on top of cylinder with dimensions of…

Q: A cylinder is inscribed in a right circular cone of height 5 and radius (at the base) equal to 7.…

A: Consider the diagram below. Assume H = 5 and R= 7 be the height and base for the right circular cone…

Q: A cylinder is inscribed in a sphere with radius 4. Find the height h of the cylinder with the…

A: given radius of sphere  R = 4. r is the radius of cylinder inscribed. and h be the height of…

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Q: A cylindrical can, open at the top, is to hold 800 cm³ of liquid. Find the height, h, and the…

A: As we know that the volume of the cylinder is: v=πr2h Given: v=800cm3 So, 800cm3=πr2hh=800πr2....(1)…

Q: cylinder is inscribed in a right circular cone of height 8 and radius (at the base) equal to 5.5.…

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Q: A cylinder is inscribed in a right circular cone of height 5.5 and radius (at the base) equal to 6.…

A: Please see the white board for the pictorial depiction of the question.H = height of the right…

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

A: Find the radius r, of the cylinder that produces the minimum surface area.

Q: An open box is to be made from a piece of cardboard measuring 10 in by 8 in. Calculate the maximum…

A: Consider the height of the box to be x inches. The length and width of the box is reduced by the…

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

A: total vol. of solid = 43πr3+πr2hwhere r=radius of cylinder and sphereh=height of cylinderGiven that…

Q: Water pours into a conical tank (an inverted cone) of height 10 m and radius 4 m at a rate of 6 m…

A: To find: The rate of water level rising when the level is 5 m high. Given: The height of the tank is…

Q: e radius of the cylinder that produces the minimum surface area

A: Given that : The total volume of the solid is 10 cubic centimeters.

Q: Q5/ A right-circular cylinder is to be inscribed in a right-circular cone of radius 2 ft and height…

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

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

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

A: solid =  one cylinder + 2*semi-sphere

Q: A cylindrical container has one end opened and the other end closed. It has a circular base of…

A: We will use Calculus to maximize the volume of the cylindrical container using the given constraint…

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

A: