Find the volume of the torus formed by revolving the circle x2 + y2 = a2 about the line x = b(b > a). (Use circular ring method).

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Q: Find the volume of the solid that results when the region enclosed by y = Vr, y = 0, and r = 81 is…

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Q: Find the volume of the solid obtained by rotating the triangle with the vertices A(0,0), B(4,4) and…

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Q: Find the volume of the solid whose base is given by 9. whose cross-sections perpendicular to the…

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Q: Find the volume of the solid formed by rotating the region inside the first quadrant enclosed by…

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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: Find the volume of the solid whose base is the semicircle y = √9 - x² where -3 ≤ x ≤ 3, and the…

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Q: Derive the formula for the volume of a sphere of radius r by slicing.

A: We have, a sphere of radius r. The differential element shown in the figure is cylindrical with…

Q: Find the volume of the solid formed by rotating the region enclosed by y = x3 and y = 4x in the…

A: We first sketch the region using a graphing calculator  y=x3 (blue) y=4x (green) The shaded region…

Q: Calculate the volume generated by the circle x^2 + y^2 -4x=-3 that revolves around ox

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Q: Find the volume of the torus generated by revolving the region bounded by the graph of the circle…

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Q: Find the volume of the solid whose base is an isosceles triangle (with base 6 meters and sides 5…

A: Given a solid whose base is an isosceles triangle (with base 6 meters and sides 5 meters) and whose…

Q: Find the volume of the solid formed by rotating the region enclosed by y=x3and y=4x in the first…

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Q: A welder decides to make a pyramid out of flat steel. The height of the pyramid is to be 3.0 ft and…

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Q: Find the volume of the smaller wedge cut from a sphere of radius 10 by two planes that intersect…

A: Here we have to find the volume of the similar wedge cut from a sphere of radius 10 by two planes…

Q: Two identical spheres are placed so that one is on top of the other inside a right circular cylinder…

A: This question is related to cylinders and spheres, we will solve it using given information.

Q: Find the volume of the solid whose base is the semicircle y = /25 – x² where –5 < x < 5 and the…

A: Given the base of the solidy=25-x2 , y&gt;0The intersection of the base with the x-axis :Put y =…

Q: Find the volume of the solid that results when the region enclosed by y = Vr, y = 0, and a 9 is…

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Q: Find the volume of the torus generated by revolving the circle (x−5)2+y2=4 about the​ y-axis. What…

A: Here, equation of circle is: (x-5)2+y2=4 So, the centre of the circle is (5,0) and radius will be 2.…

Q: Consider a right-circular cylinder of diameter 1. Form a wedge by making one slice parallel to the…

A: The diameter of the right circular cylinder is d=1. The angle which is made by other slide to the…

Q: Find the volume of the solid obtained by rotating the region enclosed by y=x^2, y=3x about the line…

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Q: Find the Volume enclosed by N = x2+y² and

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Q: In order to find the volume obtained by revolving the region enclosed by y = Vxe-* and y =…

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Q: Find the volume of the solid obtained by rotating the region enclosed by y=x^2, y=6x, about the line…

A: We know that,

Q: Find the volume of the region cut from the solid sphere ρ≤ a by the half-planes θ = 0 and θ = π/6 in…

A: Find the volume of the region cut from the solid sphere.

Q: A square pyramid whose base width is óm has an altitude of 12m is cut by a plane parallel to the…

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Q: What is the volume obtained by revolving the are biunded between the lines y=x, y=2x and x=4   about…

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Q: Find the volume of the largest circular cone that can beinscribed in a sphere of radius r.

A: Let the largest circular cone that can be inscribed in a sphere of radius r as shown below: OC=OA=…

Q: Find the volume of the solid cut from the first octant by the surface z=4-x2-y.

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Q: The base of a solid circular with a radius of 4 cm. Determine its volume if every plane…

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Q: Find the volume generated by revolving the plane area generated by the equations y = ex^2, y=0, and…

A: To find the volume of solid formed when the region bounded by y=e-x2, y=0 and  x=0  about the…

Q: Find the volume of the solid enclosed by y = x² + 1, y = 9 – x² and rotated about the y-axis.

A: Suppose a region is enclosed by two curves y=fx and y=gx. To calculate the volume of the region…

Q: a truncated hexagonal right prism has an average lateral edge of 24cm. what is the volume of the…

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Q: Find the radius and height of a cylindrical soda can with a volume of 354 cm3 that minimize the…

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Q: Find the volume of the solid obtained by rotating the region enclosed by y=x^3, y=9x, x≥0 about the…

A: The equation of curve y=x3 , y=9x and x≥0 Washer method formula  To draw graph

Q: Find the volume of a sphere. 4/3piR^3 using cylindrical shells

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Q: rated by revolving the area bounded by the parabola y² = 8x and its latus rectum about the latus…

A: Introduction: The chord that passes across the focus of a parabola and is perpendicular to the…

Q: What are the dimensions of the lightest open top right circular cylindrical can that will hold the…

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Q: Find the volume of the torus obtained by revolving the circle x^2 + y^2 = 4 about the line x = 3.

A: Find the volume of the torus obtained by revolving the circle x^2 + y^2 = 4 about the line x = 3.

Q: By Sketching the graph, find the volume of the solid generated by revolving the region given by, y =…

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Q: Find the volume of the solid generated by revolving the shaded region about the given axis.

A: We need to find volume.

Q: Find the volume of the solid. y=9-x2, y=0, about the x-axis

A: The given solid is bounded between the curve y=9-x2, y=0,  rotating about the x-axis. Volume of the…

Q: Find the exact volume of the solid of revolution that results when a rectangular region with…

A: Given data: When the rectangle is rotated about its length then the revolution gives the right…

Q: Find the volume of the solid generated when the region enclosed by y = sqrt(x+1), y = sqrt(5x), and…

A: The volume of the region bounded by the curves y1(x) and y2(x) is given by the formula…

Q: Engr Thomas Pendot wants to construct a frustum from a right circular cone. At what distance from…

A: Let h be the distance from the base of the right circular cone which also the height of the frustum.…

Q: Two identical spheres are placed so that one is on top of the other inside a right circular cylinder…

A: topic - volume of cylinder

Q: Find the volume of the portion of the solid sphere ps8 that lies between the cones o= and ф %3D 3 3…

A: The portion of the solid sphere ρ≤8 that lies in between the cones ϕ=π3  and  ϕ=2π3

Q: Find the volume of the solid obtained by rotating the region enclosed by 30 y = x?, y = 5x, about…

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Q: By Sketching the graph, find the volume of the solid generated by revolving the region given by, y =…

A: If is a function, then the independent variable x is called the input of the function and the…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.