Maximum Area Find the dimensions of the largest rectangle that can be inscribed in a semicircle of radius r (see Exercise 25).

Q: Optimization An open-top rectangular box is to have a square base and a surface area of 100 cm2.…

A: Given: Surface area of an open top rectangular box = 100 cm2. To find: We have to find the…

Q: A gas station stores its gasoline in a tank under the ground. The tank is a cylinder lying…

A: I am attaching image so that you understand each and every step.

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: 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: 2) The volume of an open box with a square base is 4,000 cubic centimeter (cc). Find the dimensions…

A: The volume of an open box with a square base is 4,000 cubic cm.

Q: SHOW FULL SOLUTION. A semi-circle is placed on top of a rectangle such that the diameter of the…

A: Given :   A semi-circle is placed on top of a rectangle such that the diameter of the semi-circle…

Q: Maximum-volume box Suppose an airline policy states that allbaggage must be box-shaped with a sum of…

A: Modeling of the problem: As the base is square base , let the three dimensions be x, x and y. Since…

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: 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: A field next to a building needs to be enclosed by a fence. A total of 500 feet of fencing is…

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Q: A rectangular area is enclosed by 144 feet of fencing. What dimensions will maximize the fenced…

A: A rectangular area is enclosed by 144 feet of fencing. That is, The perimeter of the given…

Q: Minimum Cost An industrial tank of the shape described in Exercise 33 must have a volume of 4000…

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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: Circle in a triangle What are the radius and area of the circle ofmaximum area that can be inscribed…

A: Given Data The two equal sides of the isosceles triangle is a=b=1.   Consider the third side of the…

Q: A box with an open top has vertical sides, a square bottom, and a volume of 256 cubic meters. If the…

A: Solution: Let x is the base of the box Let y is the width of the box Let z is the height of the box…

Q: Maximum-volume cylinder in a sphere Find the dimensions ofthe right circular cylinder of maximum…

A: We have to find the dimensions of the right circular cylinder of maximum volume that can be placed…

Q: 47. Minimum material. A rectangular box with no top and two parallel partitions (see the figure)…

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Q: 10. An open box is to be made by cutting a square from each corner of a 12-inch-by-12-inch piece of…

A: Suppose the side of the square to be cut off from each corner is "x" inch. Therefore, the length of…

Q: Arectangular lot is to be enclosed with a fence. A building is on one side of the lot, so it won't…

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Q: 8. Arectangular field is to be bounded by a fence on three sides and by a straight stream on the…

A: Let be the length of the side parallel to the stream and let be the length of the side…

Q: A closed cylindrical container has a surface area of 400cm². Determine the dimensions for maximum…

A: A function will have a maximum at a point where the value of the first derivative of the function…

Q: A box with an open top has vertical sides, a square bottom, and a volume of 32 cubic meters. If the…

A: GIVEN DATA : A box withe vertical sides and base of the base is square                         The…

Q: 5. A trough with trapezoidal cross-section is to be made from a 1,000 cm by 40 cm rectangular sheet…

A: A trough with trapezoidal cross-section is to be made from a 1,000 cm by 40 cm rectangular sheet of…

Q: 8. A rectangular box with no top is to be made from a piece of cardboard that is 20 ft by 20 ft.…

A: Dimension of cardboard=20ft by 20ft

Q: A rectangular lot is to be enclosed with a fence. A building is on one side of the lot, so it won't…

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Q: APPLICATION: 1. A pigpen is to be enclosed using 640 m of fencing along three of its sides, the…

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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 rectangular garden is to be fenced off along the side of a building. No fence is required along…

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Q: pyramid 3 m high has a square base that is 3 m on a side. The crosssection of the pyramid…

A: The pyramid is 3m high. Base of the pyramid is a square of side 3m. The cross section is also a…

Q: A trough is 4 meters long, 2.5 meters wide, and 2 meters deep. The vertical cross-section of the…

A: Given data, A trough long = 4 meters width (base) =2.5 meters Depth (height) = 2 meters. Density =…

Q: An open box is to be made out of a 6-inch by 14-inch piece of cardboard by cutting out squares of…

A: Cardboard with x2area cutouts is  Volume of the box , V = l w h cu.units Where length = 14 -2 x…

Q: A rectangular box with an open top and one partition is to be constructed from 288 square inches of…

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Q: A trough is 6 meters long, 2.5 meters wide, and 4 meters deep. The vertical cross-section of the…

A: Given data: *The length of trough is L=6 m *The width of the trough is w=2.5 m *The depth or the…

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

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Q: A box with an open top has vertical sides, a square bottom, and a volume of 108 cubic meters. If the…

A: A box with an open top has vertical sides, a square bottom Let's assume length of box =x Since, base…

Q: 24. An open box is to be made by cutting a square from each corner of a 20-cm-by-32-cm piece of…

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Q: Find the dimensions of the rectangle of maximum area that can be inscribed in a circle of radius  r…

A: To find the dimensions of the rectangle

Q: An open box is to be made out of a 12-inch by 14-inch piece of cardboard by cutting out squares of…

A: Given: The size of cardboard is 12-inch by 14-inch  To find the dimension of the resulting box that…

Q: A rectangle has one side on the x-axis and two corners on the top half of the circle of radius 1…

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

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Q: Using Lagrange multipliers Find the maximum area of a right triangle whose perimeter is 4. Note:…

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Q: A rectangular solid with a square base has a surface area of 121.5 square centimeters. (Let w…

A: Let w represent the width of the sides of the square base and h represent the height of the…

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

A: Part (a) -

Q: How do you solve the question in the attached picture?

A: Consider the figure, The base of the rectangular solid is square.  Also, the total surface area is…

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

A: Given: Volume = 4 m3