20" 25 (a) 25 - 2x 20 - 2x (b) Figure 4.38 An open box made by cut- ting the corners from a piece of tin. (Example 3)

Q: A window is in the form of a rectangle surrounded by a semi-circular opening. The total perimeter of…

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

Q: 4. A right circular cylinder of height h = 2x is inscribed in a sphere of fixed radius R. (a) Show…

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Q: 9 A right circular cone is inscribed in a sphere with radius r and the height of the cone is h cm.…

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Q: An open box is to be made out of a 10-inch by 20-inch piece of cardboard by cutting out squares of…

A: Draw the diagram for the given problem for the given conditions and then find the volume

Q: A woman at a point A on the shore of a circular lake with radius R kilometer wants to arrive at the…

A: Total distance travel by the women if she row from A to C and walks from C to B. Total distance…

Q: 5. Design a 4m³ open-top box shaped like a circular cylinder as shown in Figure. What dimensions…

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Q: 5. Assume an American football has an ellipsoid shape and has a length of 27 cm and a height of 16…

A: Length in x-direction = 27cm    The point endsheight in  y-direction = 8cmheight in  z-direction =…

Q: Find the maximum volume of sphere that may be completely submerged in a cone of height 5 m. Express…

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

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Q: A window on a new house is designed as a rectangle with a semicircle on the top. If the window is…

A:

Q: A waterway in a theme park has a semicircular cross section with diameter 11 ft. The boats that are…

A: Consider the figure for the water way and the boat. The circumference of the boat is the equation of…

Q: A box with an open top is to be constructed from a square piece of cardboard with dimensions 4 cm x…

A: 1/

Q: B A A cone-shaped cup is made from a circular piece of paper of radius 7 by cutting out a sector and…

A:

Q: 1. A long metal sheet with a width of L meters is formed into a gutter by bending up two of its…

A: A roof gutter is to be made from a long strip of sheet metal L units wide, by bending up equal…

Q: 15. A open-top box is to be made from a 24 in by 36 in piece of cardboard by removing a square from…

A: To find: The size of square to be cut of each corner to get a box with maximum volume. Given: The…

Q: An open rectangular box of volume 400 cubic inches has a square base and a partition down the…

A: To Determine: Find the dimensions of the box for which the amount of material needed to construct…

Q: An open box is to be made from a 6 ft by 16 ft rectangular cardboard by cutting out equal squares…

A: Find the maximum volume  by derivative

Q: 3. A rectangle with a fixed perimeter of 64 units is rotated about one of its sides, thus sweeping…

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Q: A cardboard box manufacturer wishes to make open boxes from pieces of cardboard 12 cm square by…

A: Assume length of corner cut = x

Q: A box with an open top is to be constructed from a square piece of cardboard with dimensions…

A:

Q: 4. A rectangular box is to be made from a piece of cardboard 15cm by 24 cm by cutting equal squares…

A: A rectangular box is to be made from a piece of cardboard 15 cm by 24 cm by cutting equal squares…

Q: The diagram shows a square prism with cross-section x units by x units, and length (9- 2x) units.…

A: We know that the volume of a square prism is equal to its base area X the height. first of all we…

Q: n constructing an open rectangular box from 108 ft? of material, what dimensions will result in a…

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Q: A box with an open top is to be constructed from a rectangular piece of cardboard with dimensions 8…

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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 right circular cone has a base diameter of 24 cm. The maximum area of parabolic segment that can…

A: Use the following formulae, to obtain the solution. Area of Parabolic Segment=23bhVolume of the…

Q: 2. An open box is to be made from a square piece of material, 24 inches on a side, by cutting equal…

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Q: An open box is to be made from a 21 ft by 56 ft rectangular piece of sheet metal by cutting out…

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Q: A trough with trapezoidal cross sections is formed by turning up the edges of a 30-inch-wide sheet…

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Q: 7. Find the area bounded by a parabola and any right chord. (Use the parabola = 4az, chord z= 21.)…

A: Given: To find the area bounded by a parabola Formula used: The area under the curve y=f(x) from…

Q: Equal squares are cut from the corners of a cardboard, 16 cm wide and 30 cm long. an open box is…

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Q: An open box is to be made from a 3 ft by 8 ft rectangular piece of sheet metal by cutting out…

A: We need to find maximum volume.

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

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A:

Q: A right circular cylinder that is open on both ends is inscribed in a sphere of radius a . What is…

A: Given Data: The radius of the sphere is: a   From the figure, Using Pythagoras rule,…

Q: (23) A right triangle with a hypotenuse of 6 inches is rotated about one of its legs to generate a…

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Q: A right triangle with hypotenuse of 5/3 inches is revolved about one of its legs t generate a cone.…

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Q: 2. A 27-in gutter is bent on two sides as shown. Find the r and o values that will maximize the area…

A: From the given diagram:The cross-sectional area…

Q: 1. An open-top box with a square base is made from a cardboard of area 75 cm². Find the maximum…

A: given area is 75cm2find the maximum volume of the box

Q: 15. A rancher will use 600 m of fencing to build a corral in the shape of a semicircle on top of a…

A:

Q: here having a radius of 3cm. is cut in the shape of a circular cone of maximum volume. is the…

A: Topic:- application of derivatives

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

A:

Q: Find the dimensions of the open rectangular box of maximum volume that can be made from a sheet of…

A: We have to use the concept of derivatives

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

A:

Q: An Architect Plans To Build A Triangular Enclosure With A Fence On Two Sides And A Wall On The Third…

A: The given triangle is sketched below.

Q: The surface area of an open-top cylindrical box is 27π cm ². Determine the dimensions of the…

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Q: An architect plans to build a triangular enclosure with a fence on two sides and a wall on the third…

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Q: An open box is to be made from a 33 ft by 88 ft rectangular piece of sheet metal by cutting out…

A: Solve the given problem.

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.