explain and illustrate how you could find the volume of a sphere of radius R using the techniques of solids of revolution. set up integral that would give the volume but dont simplify

Q: I need to find the answer using integration with polar coordinates.

A: Given:

Q: Use a double integral to find the volume of the indicated solid. 8. X +y+2 8 00

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Q: y = 9x² and y = 0 about x = -4

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Explain the method of discs for finding the volume of a solid of revolution. (when the area revolves…

A: If the axis of revolution is the boundary of the plane region and the cross sections are taken…

Q: Find the volume generated by revolving the region bounded by y=−x^4+3x^3, y=0  revolving about the x…

A: The given problem is to find the volume generated by revolving the region bounded by given curves…

Q: Use a triple integral to find the volume of the solid

A: In this question, we use the triple integral in cylindrical coordinate.  Volume=∫∫∫Erdzdrdθ

Q: Sketch the solid whose volume is given by the integral and evaluate the integral. 37/2 3 L rdz dr de…

A: To find- Sketch the solid whose volume is given by the integral and evaluate the integral.…

Q: Find the volume of the solid whose base is in the first quadrant bounded by y = √√7-7x, the x-axis,…

A: To find- Find the volume of the solid whose base is in the first quadrant bounded by y = 7 - 7x, the…

Q: Explain how to use the disk method to find the volume of a solid of revolution

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Q: Sketch the solid whose volume is given by the integral and evaluate the integral. 27 18 r dz de dr

A: NOTE: Refresh your page if you can't see any equations. .

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

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Q: Set up the triple integral to find the volume inside x² + y² = 9, above z = 0, and below x + z = 4.…

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Q: 6. What is the volume generated when the area in the first quadrant bounded by the curve x? = 8y,…

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Q: @ Eualuate the inteyral taken throughout the volume o f sphere

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Q: Determine the volume of the solid formed by revolving the area bounded by y = 4ax and x= a around…

A: Consider the given curve as y2=4ax

Q: Find the volume of sphere by using Multiple Integrals

A: We will find the volume of a sphere generated by revolving the semicircle y = √ (R 2 - x 2) around…

Q: Explain the difference between the washer method and the disc method for finding the volume of a…

A: Definite integration of a volume element within appropriate limits will give the total volume of…

Q: Use a triple integral to find the volume of the solids

A: Consider the function. z=4 and z=1-r2 The radius is defined as, 0≤r≤1 And, the angle is defined as,…

Q: Use a double integral to find the volume of the indicated solid.

A:

Q: Find the volume of the colld_generated by. revolving the area bounded by the given curves_ about the…

A: We need to find volume.

Q: y = 9x² and y = 0 about x = −4

A: Given:        y=9-x2 and y=0         x2=9           x=3 about x=-4

Q: Derive the formula for the volume of a sphere by revolving about the x-axis, the region bounded by…

A: We have to derive the formula for the volume of a sphere by revolving about the x-axis, he region…

Q: Get the volume of solid of revolution. Using Circular Disk Method.

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Q: Show by integration that the volume of a sphere of radius r is V=4/3 πr³

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Q: A hole is drilled through the center of a metal sphere of radius 6cm. The hole has a radius of 3cm.…

A: Volume of metal ring = 798.63 cm³

Q: Each integral represents the volume of a solid.Describe the solid.

A: To evaluate: ∫042π6-y4y-y2dy Solution: Evaluating the integral,…

Q: Use a double integral to find the volume of the indicated solid. 8 X + y +z = 8 24 2 8 8.

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Q: y = x4; and y = 1 about y = 2

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Q: What is the volume of the solid generated when the region surrounded by y = vx, y = 2 and y = 0 is…

A: Given: y=x,  y=2  and  y=0Rotation around y−axis

Q: Use a double integral to find the volume of the indicated solid. z = 9– 2 y 2 y=2 4 x=4

A: Given:

Q: 6. What is the volume generated when the area in the first quadrant bounded by the curve x2 = 8y,…

A:

Q: Find the volume of the solid when the area contained by y=x and y=x3 is resolved around y=3/2.

A: We graph the curves using a graphing calculator

Q: Find the volume cut from the sphere radius r = 15 by the cone ki+

A: To compute the volume using spherical coordinates, use the following formula. V=∭r2sinθdrdθdϕ

Q: write a triple integral that calculates the volume for a cylindrical surface  estimate the volume…

A: Consider the cylinder along z axis and radius 4 bounded below by xy-plane and bounded above by z…

Q: The solid S has a base described by the circle 9 x² + y² = Cross sections perpendicular to the 16…

A:

Q: Determine the volume of the solid formed by revolving the area bounded by Y- = 4ax_and x= a around…

A: The area is bounded by the curves y2=4ax and x=a around x=9.1

Q: Find the volume when the area in y = 2x^2 − 8x + 12 and y = −2x + 12 is 9 sq units and revolves…

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Q: 3. Find the volume generated by revolving the area bounded by the parabola y² = 8x and its latus…

A: Note:- As per our guidelines, we can answer the first part of this problem as exactly one is not…

Q: How do I find the radius for the methods of  volume using disks, washers and shells?

A: (1) For Disk method: The shaded region in the graph is revolving about x- axis. The radius for the…

Q: Find the volume of revolution obtained by revolving the area bounded by x = 0, 16x? + 9y² = 144…

A:

Q: Find the volume formed by rotating the region enclosed by: y = x³ + 1, the y-axis, and y = 9 about…

A: We will use the disk method to evaluate the volume of the solid of revolution.

Q: Use a double integral to find the volume of the indicated solid. 16 15 z 16- X-y 14

A: We are given the following. So, we have 0≤z≤16-x-y,  x≤y≤8, 0≤x≤8.

Q: and the x-axis. What is the volume generated by revolving this area by the у-аxis.

A: To find the volume about y axis

Q: Determine the volume of the solid of revolution formed by revolving the area bounded by y = 4ax and…

A: To obtain the volume of a solid by rotating the region bounded by two curves x=fy and x=gy about the…

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

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Q: What is the volume of the solid of revolution generated by rotating the area bounded by y%3D2, y3 3,…

A:

Q: use a double integral to find the volume of the indicated solid.

A: Introduction: The volume beneath the surface z=f(x,y) over the region D can be deduced from 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.