Consider a rectangular box B that has a bottom and sides but no top and has minimal surface area among all boxes with fixed volume V = 64 m3•

Q: Find the area of the circular washer with outerradius 2 and inner radius 1, using Fubini’s Theorem

A: Given Circle with radius ‘2’  Circle with radius ‘1’

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: Find the volume of the 'ice-cream' that is bounded by x2 + y2 + z2 : = 35 and the upper cone z2 =…

A: The given problem is to find the volume of the ice cream that is bounded by given surfaces. Given…

Q: Find the volume of solid lying in the first octant bounded by the graphs of : z = 4 – x2 – y² , y =…

A: The volume of the solid in first quadrant is given by: V=∫ab∫cdf(z)dydx Now, find the range of the…

Q: Find the volume of the solid of revolution formed by rotating each bounded region about the…

A: The volume of Revolution about x -axis is given by  V = ∫x=ax =b π y2 dx  Given,  y = x32  x = 4 and…

Q: The boundary of a lamina consists of the semicircles yV1- x2 and y- V36 - x2 together with the…

A: • This is a problem of application of double integrals. The detailed solution is explained in the…

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: Find the volume of the solid bounded by

A: Given,        z=-6+x2+y2,   and    z=6-2x2-2y2

Q: Find the volume of the solid of revolution formed when the area of the region bounded by y3Dx2,…

A:

Q: find the centroid of volume if the volum is equal to 7/15 π

A:

Q: What is the volume of the solid whose 1 30 cross-sections are squares perpendicular to the x-axis…

A: Given: The region bounded by the curves are: y=x and y=x The cross-sections are squares…

Q: Find the volume of the solid whose base is bounded by the circle x2 + y2 = 16 and whose cross…

A:

Q: Find the center of mass of a thin rectangular plate cut from the first quadrant by the lines x = 6…

A:

Q: 10. Find, among all right circular cylinders of fixed volume V, the one with smallest surface area…

A:

Q: Find the volume of the region under the surface z and above the triangle in the xy-plane with 1+ x²…

A: We have to find the volume of the region under the surface.

Q: Find the volume of the solid above the triangle with vertices (0, 0), (1, 0) and (1, 2), below the…

A:

Q: Calculate the volume of the solid bounded by the cone z2=x2+y2 and the cylinder x2+y2=4

A: Explained below

Q: Calculate the volume of the solid bounded by cone z2=x2+y2 and cylinder 4=x2+y2.

A:

Q: Compute the volume lying inside the sphere x2 + y? + z2 = 35 but outside of x² + y? = 19.

A:

Q: Find the volume in the first octant between z=9-x^2-y^2 and the cylinder x^2+y^2=1.

A: The given surfaces can be plotted as follows: Thus, the required solid will be R=x, y, z: 0≤x≤1,…

Q: Find the dimensions of the box with volume 1728 cm3 that has minimal surface area. (Let x, y, and z…

A:

Q: Find the volume of the solid generated by revolving about the line x = 2, the area bounded by y =…

A: The equation of the curves are  C1: y = x2C2: x= 2C3: y = 0 The axis of the revolution is x = 2 To…

Q: 3. Show that a closed right circular cylinder of given surface has maximum volume if its height…

A: Let r, h be the radius and height of the cylinder respectively and V, S be the Volume and Surface…

Q: 3. Find the volume of a sphere with radius r by integration.

A:

Q: Find the center of mass of solid revolution if an area in Ist Quadrant (Kuadran Pertama) bounded by…

A: Given functions are Intersection points Area of region is Centre of mass revolution

Q: Find the volume of the solid of revolution generated by revolving the region bounded by the graphs…

A:

Q: Find the mass of a lamina with density 8(x, y) = 3x, bounded by y = -x, 1 = 0 and a = 4 - y 2.

A:

Q: Find the volume generated by rotating the area bounded by each set of equations around the x-axis.…

A: The volume for solid of revolution for a curve is the volume of object determined by a curve fx…

Q: Find the volume of solid lying in the first octant bounded by the graphs of : z = 4-x2-y2, y= 2-2x2,…

A:

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: Calculate the total mass of a circular piece of wire of radius 4 cm centered at the origin whose…

A: Since, we have to calculate the total mass of a circular piece of wire ofradius 4 cm centred at the…

Q: 10. Find the center of mass of a thin rectangular plate cut from the first quadrant by the lines x =…

A: Given density δ(x,y)=3x+yWe need to first mass using formula:M=∬RδdAAccording to the problem, we…

Q: A solid lies between two parallel planes 5 feet apart and has a volume of 45 cubic feet. What is the…

A:

Q: Calculate the mass of the solid, in the first octant, bounded by the coordinated planes and the plan…

A:

Q: Calculate the volume of solid Q limited by surface z

A: Consider the solid Q: Clearly, 0≤z≤11+x2+y2Let x= r cos θ       y=r sin θ⇒x2+y2=r2Projection on the…

Q: Find the volume of the region under the surface z = and above the triangle in the xy-plane with 1+x2…

A:

Q: Find the volume of the solid bounded by the graphs of the equations: z = 3x + 3y?, x - y+1 = 0, 3x +…

A: This question is about application of intergal calculas

Q: Find the volume of the solid of revolution bounded by the circle +y = 16, and the lines 0 and

A: To find: Volume of the solid

Q: Find the volume of the region above the triangle with vertices (1,0), (0,1) and (3,1), below the…

A: Given Data: fx,y=x2y The vertices of the triangles are (1,0), (0,1) and (3,1).

Q: . Find the volume bounded by z = 9 –x² – y² and z = 0. Give a numerical %3D answer.

A: Given that the region is bounded by z=9-x2-y2 and z=0. We know that the volume bounded between…

Q: 1) z = 2 – x² – 2y², z = 1

A:

Q: find the volume “V” obtained by revolutionizing the region between y=x2  and y=12-x around the axis…

A:

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

A:

Q: A hole is drilled through the center of a ball of radius r, leaving a solid with a hollow…

A: Given  that the center of a ball of radius r;  and  the  height of the cylinder be…

Q: Find the mass of a circular cone of height b and radius of base a whose density varies as the…

A: To find: The mass of a circular cone. Given information: The height of the cone is b and base is a…

Q: he volume bounded by y = x², y = 0 and x = 2 rotated about the specified = specified orientation of…

A:

Q: Find the dimensions of the box with volume 1728 cm3 that has minimal surface area. (Let x, y, and z…

A: Volume of box = xyz Surface area = 2xy+ 2yz+2zx

Q: Find the center of mass of a thin plate of constant density δ covering the given regions. The…

A:

Q: Find the volume of the 'ice-cream' that is bounded by x² + y2 + z2 = 10 and the upper cone z2 = 4x2…

A: