(a) COMPUTE the dimensions of the rectangular box of maximum volume that can be x² + y? + z? = 4. inscribed inside the sphere (CLO-2)

Q: The base of a three-dimensional figure is bound by the line y = √x + 2 on the interval [-1, 1].…

A: We have to find the volume of bounded region in the interval [-1,1].

Q: 13) Find an equation of the plane that is through the point (1.1.2) and makes minimum volume in the…

A: The equation of plane is given as, z-z0=ax-x0+by-y0 The points (1,1,2) is given Now substituting for…

Q: What are the dimensions of a closed rectangular box that has a square cross section, a capacity of…

A: x= 5.07 in y= 5.07 in

Q: 28 The region in the first quadrant bounded by y rotate about the line x = 4x2 , 3x + y = 7, and the…

A: It is given that, the first quadrant bounded by y=4x2,3x+y=7 and the y-axis is rotate about x=-4.…

Q: 2. Find the volume of the solid lying under the elliptic x2 paraboloid + 4 y2 +z = 1 and above the…

A: The elliptic paraboloid can be expressed as z=f(x,y) where fx,y=1-x24-y29. We have to notice that…

Q: 9 A copper sheet with 16 cm by 16 cm dimension has to be made as a square box with no top cover.…

A: Dimension of the copper sheet = 16 by 16 cm;                    Square corners…

Q: 11. The solid whose base is the region bounded by the semicircle y = V1 - x² and the x-axis, and…

A:

Q: A company wishes to manufacture a boxwith a volume of 36 ft3 that is open on top and is twice as…

A: Let the dimensions of the box be, length=lwidth=wheight=h It is given that length is twice its…

Q: Use Lagrange multipliers to find the dimensions of a cylindrical can with a bottom but no top, of…

A:

Q: 6. A bax with a square base is to have an open top. If the lateral surface of the bax is 100 cm",…

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Q: 4. Find the volume of the wedge cut from the first octant by the cylinder z = 12 - 3y2, and the…

A: We have to find volume.

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: Find the volumes of the solids whose bases are bounded by the graphs of y = x + 3 and y = x² - 3,…

A: So points are ( -2 , 1 ) and ( 3, 6 )

Q: 3 27 Find the center of mass of a thin plate of constant density & covering the region bounded by…

A: Center of mass of a body is a point at which it can be considered that entire mass of body is…

Q: Suppose a cylindrical package has height h and a base with a radius r. Find the values r and h that…

A: Solve the following

Q: What are the dimensions of a closed rectangular box that has a square cross section, a capacity of…

A:

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 lamina is in the shape of the region bounded by the lines x = 1 and y = 2, and the parabola y =…

A: Let's find.

Q: Find the dimensions of a cylinder of volume 1 m3 of minimal costif the top and bottom are made of…

A: The formula to find the volume of the cylinder is given below: V=πr2h where V represents volume, r…

Q: 10. Find the volume of the solid whose base is bounded by the graphs of the equations given below…

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Q: 9. A copper sheet with 16 cm by 16 cm dimension has to be made as a square box with no top cover.…

A:

Q: 2. A rectangular box has a square base with edges at least 10 cm long. It has no top, and the total…

A:

Q: The triangular region Ω has vertices (1, 1), (2, 0), and (2, 3).

A: My=∫12∫-x+22x-1kx2dydx

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 box manufacturer wishes to construct a closed box of volume 288 in ^3 where the base is a…

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Q: 6. Find the volume inside the paraboloid z = 9-x² - y², outside the cylinder x² + y² = 4, above the…

A: Relation between rectangular and polar coordinate  x=rcosθy=r sinθx2+y2=r2θ=tan-1yxdxdy=rdrdθ

Q: Example 2.4.2. Find the volume of the solid of revolution of the region enclosed by the parabola y =…

A: Topic = Application of integration

Q: Find the dimensions of a cylinder of volume 1 m 3of minimal costif the top and bottom are made of…

A: Given: Find the dimensions of a cylinder of volume 1 m 3of minimal cost if the top and bottom are…

Q: Example 8: Find the volume of the solid whose base is bounded by y = x +1 and y = x², the cross…

A:

Q: Use the result of Exercise 37 in Section 6.1 (or the exercise above if your answer is correct) to…

A: Find the volume V of the solid obtained by revolving about the line y=-3 the region between the…

Q: 5. Find the volume under the paraboloid z = -x² – y², and above the cone z = -. -V#²+ y².

A: Given

Q: Two factories are located at the coordinates (-x, 0) and (x, 0), and their power supply is at (0,…

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Q: Example 1: Determine the volume of the solid obtained by rotating the region bounded by f(x)=x² –…

A: Given function   Graph the given function using graphing calculator . Also graph x=1 and x=4…

Q: A closed rectangular box with faces parallel to the coordinate planes has one bottom corner at the…

A: Let x , y, z donate  the length, width and the height of the rectangular box.  Volume of the box is…

Q: A rectangular box has three of its faces on the coordinate planes and one vertex in the first octant…

A: Given,The box's volume is  V = xyz  but we know that   z = 4 − x2 − y2V = xyz    = xy ( 4 − x2 − y2…

Q: Compute for the volume of the solid formed bounded by the equations (y- 4)2 = x - 3, x-10, y-4, and…

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Q: Show that the rectangular box of maximum volume that can be inscribed in the sphere x^2 + y^2 + z^2…

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Q: - Find the volume of the solid that is bounded above by the cylinder z = 4-x2, on the sides by the…

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Q: 13. Find the dimensions of the closed cylinder volume V=16n that has the least amount of surface…

A: Let the radius of the cylinder be: r Let the height of the cylinder be: h Therefore the volume of…

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

A:

Q: Use Lagrange multipliers to find the dimensions of a box with volume 1000 cm3 that has minimal…

A: the surface area of the box is  S=2xy+2yz+2xz................(1) the volume of the box is given by…

Q: What are the dimensions of a closed rectangular box that has a square cross section, a capacity of…

A: Here we want to find the dimensions of the given rectangular box having volume of 101 in³ it is…

Q: 2. You wish to construct a topless crate with a surface area of 230in² and the base with one side…

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Q: 3. A closed right circular cylindrical tank is to have a capacity of 1287 m. Find the dimensions of…

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Q: A box with a square base and open top must have a volume of 5,000 cm³. Find the dimensions of the…

A: Given: Volume = 5000 cm^3 The box has bottom and the sides, it does not have top.  Let us consider…

Q: A company is constructing an open-top square- based rectangular tank that will have a volume of…

A:

Q: 4 8. What is the volume of the solid generated when the region bounded by y= V4 +3x – x and y = 2 is…

A:

Q: - You are designing a 1000 cm³ right circular cylindrical can whose manufacture will take waste into…

A: Given that the volume of the right circular cylinder is V=1000 cm3 We know that the volume of the…

Q: 5. Find the volume of the solid generated by revolving about the x-axis the smaller area bounded by…

A: Solution :- As per guidelines . I do first only.