Determine the dimension of a rectanglular solid with a square base with a maximum volume of its surface is 337.5 square centimeters.

Q: Find the height of the cylinder that can be put into a cone with radius 7 cm and height 12 cm and…

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Q: Find the dimensions of a rectangle with perimeter 68 m whose area is as large as possible. Show…

A: Given:Perimeter of a rectangle is 68 m.

Q: Find the maximum and minimum volumes of a rectangular box whose surface area is 1300 cm2 and whose…

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Q: A container with square base, vertical sides, and open top is to be made from 1000 ft2 of material.…

A: Let the container has a base side "x" and height "y"

Q: A rectangular solid that has a square base has a surface area of 150 square inches. Find the maximum…

A: Given problem is : A rectangular solid that has a square base has a surface area of 150 square…

Q: A box with a square base with side length b and height h and with an open top must have a volume of…

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Q: A paper cup is to be made in the shape of a cone, having volume 3 ounces. What should the radius and…

A: Let Volume = V  Radius = r inch. Height = h inch.  Volume of cone V=13πr2hh=9πr2    ....(1)

Q: Determine the dimensions of a rectangular box, open at the top, having a volume of 32 ft³, and…

A: Determine the dimensions of a rectangular box, open at the top, having a volume of 32 ft³, and…

Q: what are the dimensions of the right hexagonal prism of minimum surface whose volume is 36 cubic…

A: This is a problem of optimization.

Q: Find the dimensions of a cylindrical can with a bottom but no top of volume 4 m3 that uses the least…

A: To Find: Dimension of a cylindrical can with a bottom but no top of volume 4 m3that uses the least…

Q: A rectangle with perimetee 18 cm is rotated about one of its sides forming a a right circular…

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Q: Determine the dimensions of a rectangular box with a volume of 1 ft ^ 3 that has a minimum surface…

A: Given a rectangular box with volume 1 ft^3

Q: A closed box is in the shape of a rectangular solid with height 3 m. Its surface area is 268 m2. If…

A: Consider the closed box is in the shape of rectangular solid having height 3 m. The surface area of…

Q: 2. Calculate the volume of a water cylinder with total height of 10 meters and whose diameter is 400…

A: Given:height=10mDiameter=400 cmVolume of a cylinder=2πrh1m =100 cm

Q: Find the maximum and minimum volumes of a rectangular box whose, surface area is 1300 cm² and whose…

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Q: The surface area of ​​a cylindrical box with an open top is 27π ^ 2. Dimension the cylinder so that…

A: We have to find the expression for the volume first.

Q: A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the…

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Q: Of all boxes with square base and a volume of 512 cm, which one has the minimum surface area? (Give…

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Q: Determine the dimenskons of a rectangular tank, open at the top, having volume of 256cm2, and…

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Q: Determine the dimensions and surface area of a rectangular box, open  at the top, having volume V,…

A: Determine the dimensions and surface area of a rectangular box, open  at the top, having volume V,…

Q: What is the maximum volume of a cone that would fit this box?

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Q: Find the dimensions of the closed rectangular box of largest volume with surface area of 16 m². What…

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Q: Determine the dimensions of a rectangular box, open at the top, having volume V, and requiring the…

A: Let  Length=xWidth=yHeight=z Then volume of the box is  v=xyzz=vxy…

Q: Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its…

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Q: A box with a square base and open top must have a volume of 32,000 cm3. Find the dimensions of the…

A:

Q: Prove mathematically that a cylinder with hemispherical ends that has the same volume as a sphere…

A: Let r be the radius of the hemispherical end. Let h be the height of the cylinder. Let r' be the…

Q: West Coast Customs is constructing a closed-top, square-based, rect- angular subwoofer box that will…

A: Here we use application of derivatives to find the minimum surface area and find it's dimensions.

Q: Find the maximum volume of a cylindrical can such that the sum ofits height and its circumference is…

A: Let r denotes radius       h denotes height Then       volume of cylinder (V) = πr2h Restriction is…

Q: To calculate: The dimension of the rectangular solid with a square base that yields the minimum…

A: The rectangular solid has a square base. Let the dimensions of the rectangular solid be x, x and y.…

Q: A cylindrical can has a volume of 1024r cm. What dimensions yield the minimum surface area?

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Q: Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm2 and whose…

A: Find the maximum and minimum volumes of a rectangular box whose surface area is 1500 cm2 and whose…

Q: The head of a steel meat tenderizer is cube with a side length of 5 centimeters. Once face of the…

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Q: Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its…

A: Follow the procedure given below.

Q: Calculate the volume of a water cylinder with total height of 10 meters, diameter of 400…

A: Radius of cylinder = Radius of Hemisphere = R = Diameter2 = 4002 = 200 cmTotal Height of container =…

Q: A cylindrical can is to have a volume of 400 cubic centimeters. Find the dimensions (height and…

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Q: determine the dimensions of a rectangular tank open at top having the volume of 108 cm^3 and…

A: Finding the dimensions of the box using the given conditions

Q: Find the maximum volume of a rectangular box whose surface area is 1600 cm? and whose total edge…

A: By using lagrange multiplier

Q: What is the largest possible volume of a rectangular box whose diagonal has length L?

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Q: A box with a square base and open top must have a volume of 4,000 cm3. Find the dimensions of the…

A: Consider a box with square base and open Top and have a volume of 4000 cubic centimeters. Let the…

Q: Find the minimum cost of a rectangular box of volume 200 cm³ whose to

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Q: A rectangular box with no top is to have a surface area of 16 m2. Find the dimensions (in m) that…

A: Use derivative test for calculating the maximum volume of a rectangular box. Assume that base of box…

Q: . A box with a square base and open top must have a volumeof 32,000 cm cu .  . Find the dimensions…

A: To Determine: Find the dimensions of the box that minimize the amount of material used Given: A box…

Q: A rectangular solid that has a square base has a surface area of 150 square inches. Find the maximum…

A: Given that rectangular box has a square that means length and breadth are equal.Let,Length of the…

Q: Determine the dimensions of a rectangular solid (with a square base) with maximum volume if its…

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Q: A long metal sheet with a width of L meters is formed into a gutter by bending up two of its sides…

A:

Q: A box with a square base and open top must have a volume of 13,500 cm3. Find the dimensions of the…

A: To find the dimensions

Q: A rectangular tank that is 1372 ft° with a square base and open top is to be constructed of sheet…

A: The tank with minimum weight is the one with minimum surface area. Since the base is square, its…

Q: A cylindrical shampoo container is to have volume 750 cm³. Shampoo V%3DTT r?h 759cm3 ) Determine the…

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