3. Show that a closed right circular cylinder of given surface has maximum volume if its height equals the diameter of its base.

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: 4. Determine the dimensions of the cone of maximum volume that can be inscribed in a sphere of…

A:

Q: Find the surface area of the portion of the half ball with a radius a which cuts off by the cylinder…

A: To Find: The surface area of the portion of the half ball with a radius a which cuts off by the…

Q: 5. Show that the rectangular box of maximum volume inscribed in a sphere of radius r is a cube.

A:

Q: 2. Suppose that the triangle with vertices (-1,-1), (0, 1) and (1,–1) is revolved about the y –…

A:

Q: Find the dimensions of the right circular cone of minimum volume V that can be circumscribed about a…

A:

Q: Calculate the volume of the solid that is limited superiorly by the sphere x2+y2+z2=9 and inferiorly…

A: To Calculate: Volume of the solid bounded superiorly by x2+y2+z2=9 and inferiorly by x2+y2=z2.

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

A:

Q: Find the radius and height of a cylindrical can of total surface area A whose volume is as large as…

A: Find the radius and height of a cylindrical can of total surface area A whose volume is as large as…

Q: 2. The area of the parabola x2 = 4y – 4 cut through its latus rectum is revolved about the…

A: 2) Parabola; x2=4y-4End points of the latus rectum (-2,2) and (2,2)vertem = (σ 1)using washer method

Q: 7. A manufacture want to design an open box having a square base and a volume of 256 cm³. What…

A: Given problem is :

Q: A cylindrical container with circular base is to hold 64 in^3. Find its dimensions so that the…

A:

Q: 13) Find an equation of the plane that is through the point (1,1,2) and makes minimum volume in the…

A:

Q: Show that a closed right circular cylinder of given surface has maximum volume if its height equals…

A: Let, the surface area be S, radius be r, height be h and volume be V. The total surface area be…

Q: 3]. , Let V = ar²h, where V the volume of a right circular cone of radiusr and height h. Show that…

A:

Q: 3. Find the dimensions of the right-circular cylinder of greatest volume that can be inscribed in a…

A: This is a problem of the Application of differentation.

Q: In constructing an open rectangular box from 75 ft² of material, what dimensions will result in a…

A:

Q: Find the dimensions (radius r and height h) of the cone of maximum volume which can be inscribed in…

A: According to our company policy, I am supposed to answer only one question at a time so for the rest…

Q: Find the volume enclosed by the cy linder (x-1) ty²=1 and the sphere x² +y²7z²=L4.

A:

Q: Find the volume limited by the graphs of the equations

A: Part (a):

Q: Consider a rectangular box B that has a bottom and sides but no top and has minimal surface area…

A:

Q: The base of a three-dimensional figure is bound by the line x = -y2-2y +3 on the interval [0, 1].…

A: Option(4) is true

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

A:

Q: Find the surface area of the portion of the half ball with radius a which cuts off by the cylinder…

A: The equation of a ball with radius a is x2+y2+z2=a2. The surface area of the function z=fx,y over…

Q: Find the volume of the parallelepiped defined by the inequalities 0≤2x−3y+z≤5,1≤x+2y≤4,−3≤x−z≤6.

A:

Q: Find the volume of the solid whose base is bounded by the circle x2 + y2 = 9 and whose cross…

A: To find the volume of the solid whose base is bounded by the given circle and whose cross-sections…

Q: 4. Find the radius of the right circular cone with least volume that can be circumscribed about the…

A: Formula Used: Volume of Cone = 13πR2h where R,h denote the radius and height of right circular…

Q: Show that the rectangular box (including the top and bottom) withfixed volume V = 27 m3 and smallest…

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: Find the dimensions of a right cone with surface area S=4 n that has the largest volume?

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the volume generated by a parabola y2=4(51)x, its axis and its latus rectum revolves around its…

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

A:

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

A:

Q: 7. Show that a closed rectangular box of maximum volume having a prescribed surface area S is a…

A: Let the volume function be V=lbh and the surface area is 2lb+bh+lh=S. Take the constraint to be gl,…

Q: The altitude of a cylinder of maximum volume that can be inscribed in a right circular cone of…

A:

Q: Find the dimensions of the closed right circular cylindrical can of smallest surface area whose…

A:

Q: A manufacturer of food-storage containers makes cylindrical can with a volume of 500 milliliters.…

A: A manufacturer of food-storage containers makes cylindrical can with a volume of 500 milliliters.

Q: 9. Find the demensions of the right circular cylinder of largest volume that can be inscribed in a…

A:

Q: Show that the surface area of a closed cuboid with square base and given volume is minimum , when it…

A:

Q: Assume we wish to to make a right cylindrical can with a bottom and no top, and with a capacity of…

A: Solve it

Q: The base of a three-dimensional figure is bound by the line y = 6 - 2x on the interval [-1, 2].…

A:

Q: Find the volume of the largest right circular cylinder that can be inscribed in a sphere of radius…

A:

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

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Q: 6. Show that when a hole of radius a is bored through the center of the sphere of radius b, the…

A: Given : The radius of the sphere is b. The radius of the hole is a. We have to show that the volume…

Q: Find the dimensions of the closed right circular cylindrical can of smallest surface area whose…

A: According to the given information it is required to find the dimension of right circular cylinder…

Q: The area in the first quadrant bounded by a parabola 12y = x2, the y=axis, and the line y = 3,…

A: Given:       Parabola x2=12y                      y=x212              line y=3 The parabola and line…

Q: Find the dimensions of the closed right circular cylindrical can of smallest surface area whose…

A:

Q: Show that the surface area of a closed cuboid with square base and given volume is minimum, when it…

A: Let the length be x , breadth be x and height be y of a closed cuboid with a square base.So Volume…

Q: 4. West Coast Customs is constructing and open-top, square-based, rect- angular subwoofer box that…

A: West Coast Customs is constructing and open-top, square-based.rectangular subwoofer box that will…