A right circular cone is inscribed in such a way that its vertex is at the center of the circular top of the hemisphere of diameter 6 inches. Find the dimensions of the maximum volume of the inscribed cone.

Q: A rectangle has a perimeter p cm. Determine the length and breadth of the rectangle when its area is…

A:

Q: 2. An open box is to be made from a square piece of material by cutting equal squares from each…

A: An open box is to be made from a square piece of material by cutting equal squares from eachcorner…

Q: 3 Aeylindrical metal tin of radius rem is closed at both ends. It has a volume of 16000r cm’. (a)…

A: Given that  Surface area  A=2πr^2+32000π/r  To find the total surface area of the tin if maximize…

Q: Minimum-surface-area box Of all boxes with a square baseand a volume of 8 m3, which one has the…

A:

Q: 4. A line passes thru (5, 11) and cuts a right triangle with the coordinate axes in the first…

A: (1) Equation of a straight line passing through the point (x1,y1) is               y - y1 = m ( x -…

Q: An open box is to be made out of a 9-inch by 19-inch piece of cardboard by cutting out squares of…

A: The given question has been solved in detail

Q: 10. A rectangular box is to be made from 16m2 of cardboard. Use Lagrange multi- pliers to find the…

A: (10) Consider the provided question, Give that, rectangular box has to be made from 16 m2 cardboard.…

Q: total area of triangle and circle whic is obtained the maximum

A: Length of wire = 100 cm Diameter of circle = d cm

Q: An open box is to be made out of a 9-inch by 17-inch piece of cardboard by cutting out squares of…

A: topic - absolute maximum and absolute minimum  maximum volume =130.43 minimum volume =99

Q: 1. A rectangular box has a square base. The combined length of a side of the square base, and the…

A:

Q: A city is planning to replace one of its water storage tanks with a larger one. The city’s old tank…

A: we need formula for calculate the volume of cylinder:-

Q: A rectangle with base on the x−axis has its upper vertices on the curve y = 9−x2. Find the…

A:

Q: 17. Maximizing volume. From a thin piece of cardboard 20 in. by 20 in., square corners are cut out…

A: Dimensions of a thin piece of cardboard is 20 in. by 20 in. Let x in. be cut out from each corner of…

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: A rain gutter is formed by bending up the sides of a 52-in.-wide rectangular metal sheet as shown in…

A:

Q: QI/ An open storage bin with a square base and vertical sides is to be constructed from a given…

A: And open storage bin with a square base and vertical sides is to constructed from a given amount of…

Q: An open-top bin is to be made from a 32-inch by 42-inch piece of plastic by removing a square from…

A: We have given a rectangular piece,

Q: OAA We have 27 m2 of material to make a box without a top. The base of the box should be a square…

A:

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: A delivery company requires that any box delivered must have a length plus girth (distance around)…

A: GIVEN: 132 = (length + girth) = z + (2x + 2y)

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

A:

Q: we are constructing an open top box with a square base out of 24 m^2 of material. Find the dimension…

A:

Q: Maximum printable area A rectangular page in a text (withwidth x and length y) has an area of 98…

A: A rectangular page in a text (with width x and length y) has an area of 98 in2. That is,…

Q: A rectangle is place in a circle of radius r with its corner in the boundary of the circle. Find the…

A: we know that rectangle is place in a circle of radius r which encloses maximum area will be a square…

Q: A rain gutter is formed by bending up the sides of a 40-in.-wide rectangular metal sheet as shown in…

A: Given problem:-

Q: An open box is made from a square piece material with sides 3 feet by 3 feet by cutting equal…

A:

Q: A parcel delivery service will deliver a package only if the length plus girth​ (distance around)…

A: (A) Let x and y represents the length and girth of the rectangular box. Given that, the volume of…

Q: A rectangular field as shown is to be bounded by a fence. Find thedimensions of the field with…

A: Let us represent the length and width of the rectangular field as L and W. We need to maximize the…

Q: An open-top rectangular box is constructed from a 10-in.-by-16-in. piece of cardboard by cutting…

A: Given:We are given an 10x16 piece of cardboard.Let x be the length of the side of the square we want…

Q: A rectangular field as shown is to be bounded by a fence. Find the dimensions of the field with…

A:

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 rain gutter is formed by bending up the sides of a 42-in.-wide rectangular metal sheet as shown in…

A: Given that a rain gutter is formed by bending up the sides of a 42 in. wide rectangular metal sheet.

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 rectangular area is enclosed by 188 feet of fencing. What dimensions will maximize the fenced…

A:

Q: A manufacturer of transparent container makes a plastic cylindrical aquarium

A:

Q: An open box has a surface area of 20 where the box has a square base. What function should be used…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: A rain gutter is formed by bending up the sides of a 52-in.-wide rectangular metal sheet as shown in…

A: Both sides = x So the width = 52-x-x= 52-2x So the cross sectional area= x(52-2x) = 52x - 2x2…

Q: 5. An open box of maximum volume is to be made from a square piece of material, 24 inches on a side,…

A: 5 Sol:length of box = 24-2x=lwidth of box = 24-2x=wheight of box =x=hthe volume, V = (24-2x) x…

Q: There are 10 square meters of material and a person wants to construct a box. Find the maximum…

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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…

A:

Q: A box with a lid is to be made from a rectangular piece of cardboard measuring 48 cm by 144 cm. Two…

A: The figure is given by To evaluate: The value of x such that the volume of the box is maximum.

Q: Your company are designing metal trays. They will be made out of a sheet of metal which has a…

A:

Q: A cylindrical can with one end is to be made with 24π cm2 of metal. Find the dimensions of the can…

A: Given that a cylinder with one end is to be made of a material whose area is 24π cm2. To find the…

Q: A rectangular plot of farm three sides by a single-strand electric fence. With the largest area you…

A: Let the length of the rectangular plot = x and breadth of the rectangular plot = b It is given that…

Q: You are designing a glass candle holder.  It will be a rectangular prism with outer surface area 200…

A:

Q: Minimum perimeter rectangles Of all rectangles of area 100,which one has the minimum perimeter?

A: Given area of rectangle is 100 sq. unit To find the least perimeter

Q: A piece of cardboard measuring 23 inches by 23 inches is formed into an open-top box by cutting…

A:

Q: . A rectangle with base on the r axis has its upper vertices on the curve y = (a) Find the maximum…

A:

Q: A container in the shape of a right circular cylinder with no top has a surface area of 3π ft2. What…

A:

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